Computation of speed

Computation of speed

Given distance and time, speed can be computed by using the following formula:

$Speed = \frac{Distance}{Time}$

Example 1

A car travels a distance of 480 kilometres in 6 hours. Find its speed.

Solution

Apply the formula for speed:

$Speed = \frac{Distance}{Time}$

From the question, identify the distance and the time taken. That is,

Distance = 480 kilometres Time = 6 hours

Substitute the values of distance and time in the formula to get the speed of the car. That is,

$Speed = \frac{480 \text{ km}}{6 \text{ h}} = 80 \text{ km/h}$

Therefore, the speed of the car is 80 kilometres per hour.

Example 2

Edina ran 70 metres in 10 seconds. What was her speed?

Solution

Apply the formula for speed:

$Speed = \frac{Distance}{Time}$

From the question, identify the distance and the time taken. That is, Distance = 70 metres Time = 10 seconds

Substitute the values of distance and time in the formula to get the speed of Edina. That is,

$Speed = \frac{70 \text{ m}}{10 \text{ s}} = 7 \text{ m/s}$

Therefore, Edina's speed was 7 metres per second.

Example 3

A car travelled a distance of 459 000 metres in 9 000 seconds. Find the speed of the car in kilometres per hour.

Solution

Use the following steps:

Apply the formula for speed:

$Speed = \frac{Distance}{Time}$

Convert the given metric units of distance in metres into kilometres and time in seconds into hours:

1. Distance: 459 000 metres = 459 kilometres
2. Time: 9 000 seconds = 2$\frac{1}{2}$ hours

Substitute the values of distance and time in the formula to get the speed of the car. That is,

$Speed = \frac{459 \text{ km}}{2\frac{1}{2} \text{ h}} = \frac{459}{\frac{5}{2}} = 183.6 \text{ km/h}$

Therefore, the speed of the car is 183.6 kilometres per hour.

Example 4

Makungu lives at Mondo Village. Everyday, he rides his motorbike to travel a distance of 15 kilometres in 0.75 hours from the village to school. At what speed does he ride the motorbike?

Solution

Apply the formula for speed:

$Speed = \frac{Distance}{Time}$

From the question, identify the distance and time taken. That is, Distance = 15 kilometres Time = 0.75 hours

Substitute the values of distance and time in the formula to get the riding speed. That is,

$Speed = \frac{15 \text{ km}}{0.75 \text{ h}} = 20 \text{ km/h}$

Therefore, Makungu rides the motorbike at a speed of 20 kilometres per hour.

Computation of distance

The formula for speed can be used to find distance if speed and time are known.

$Speed = \frac{Distance}{Time}$

Cross multiplication in the formula for speed gives:

$Distance = Speed \times Time$

Example 1

Majaliwa rode a motorbike at a speed of 24 kilometres per hour. If he continuously rode the motorbike for 4 hours, what distance did he travel?

Solution

Use the following steps:

1. Apply the formula for distance: $Distance = Speed \times Time$

2. From the question, identify the values of time and speed. That is, Time = 4 hours Speed = 24 kilometres per hour

3. Substitute in the formula the values of time and speed to get the distance. That is, $Distance = 24 \text{ km/h} \times 4 \text{ h} = 96 \text{ km}$

Therefore, Majaliwa travelled a distance of 96 kilometres.

Example 2

A lorry travelled for 3 hours at a speed of 78 kilometres per hour. Also, it travelled for 2 hours at a speed of 84 kilometres per hour. Find the total distance covered.

Solution

Use the following steps:

1. Apply the formula for distance: $Distance = Speed \times Time$

2. From the question, identify the values of time and speed for both journeys. That is,

First part of the journey Time = 3 hours Speed = 78 kilometres per hour

Second part of the journey Time = 2 hours Speed = 84 kilometres per hour

3. Substitute the values of speed and time in the formula for both journeys to obtain the distance. That is,

First part of the journey $Distance = Speed \times Time = 78 \text{ km/h} \times 3 \text{ h} = 234 \text{ km}$

Second part of the journey $Distance = Speed \times Time = 84 \text{ km/h} \times 2 \text{ h} = 168 \text{ km}$

Total distance = Distance of first part of the journey + Distance of second part of the journey = 234 km + 168 km = 402 km

Therefore, the lorry travelled a total distance of 402 kilometres.

Computation of time

You can simply recall the formula for time using:

$Time = \frac{Distance}{Speed}$

Example 1

The distance between the first and second train stations is 96 kilometres. The speed of a train from the first to the second station is 48 kilometres per hour. What time will the train take to arrive at the second station?

Solution

Use the following steps:

1. Apply the formula for time: $Time = \frac{Distance}{Speed}$

2. From the question, identify the values of distance and speed. That is, Distance = 96 kilometres Speed = 48 kilometres per hour

3. Substitute the values of distance and speed in the formula: $Time = \frac{96 \text{ km}}{48 \text{ km/h}} = 2 \text{ h}$

Therefore, the train used 2 hours to arrive at the second station.

Example 2

A cockroach crawled a distance of 108 centimetres at a speed of 9 centimetres per second. What time did it use to cover the distance?

Solution

Use the following steps:

1. Apply the formula for time: $Time = \frac{Distance}{Speed}$

2. From the question, identify the values of distance and speed. That is, Distance = 108 centimetres Speed = 9 centimetres per second

3. Substitute the values of distance and speed in the formula: $Time = \frac{108 \text{ cm}}{9 \text{ cm/s}} = 12 \text{ s}$

Therefore, the cockroach used 12 seconds.

Example 3

A passenger train travelled from Dar es Salaam to Tabora at 64 kilometres per hour. A goods train left Tabora to Dar es Salaam at a speed of 80 kilometres per hour. Both trains left the stations at the same time. If the distance from Tabora to Dar es Salaam is 864 kilometres, how long did it take for the two trains to meet?

Solution

Steps

1. Write the formula of finding distance $Distance = Speed \times Time$

2. Total distance = 864 kilometres. Distance travelled by the first train = 64 km/h × t Distance travelled by the second train = 80 km/h × t Total distance = distance travelled by the first train + distance travelled by second train. Let t = time

$864 \text{ km} = 64t + 80t = 144t$ $t = \frac{864}{144} = 6 \text{ hours}$

Therefore, the trains took 6 hours to meet.

Example 4

One car left from Dar es Salaam to Mbeya. An hour later, another car left from the same station to Mbeya at a speed of 80 kilometres per hour. After three hours, the second car overtook the first car. Find the speed of the first car.

Solution

The second car will overtake the first car when they will have travelled equal distance. Distance travelled by the first car = distance travelled by second car. If the second car left an hour after the first car, then from the distance formula, we have:

$Distance = Speed \times Time$

Let t = Time Speed of the first car = $s_1$ Speed of the second car = $s_2$

Distance travelled by the first car = $s_1 \times (1 + t)$ Distance travelled by the second car = $s_2 \times t$

But distance travelled by the first car is equal to the distance travelled by the second car.

Thus, $s_1(1 + t) = s_2 \times t$

Since t = 3 hours, then $s_1(1 + 3) = 80 \text{ km/h} \times 3 \text{ h}$

$4s_1 = 240$

$s_1 = 60 \text{ km/h}$

Therefore, the speed of the first car was 60 kilometres per hour.