Math worksheet for Speed and Rate sums

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Speed and Distance sums

1) Station A and Station B were 109 km apart. At 7a.m., a bus left Station A and travelled to Station B at an average speed of 63 km/h. At the same time, a cyclist left Station B and cycled towards Station A at 18 km/h along the same road. How far apart were the bus and the cyclist at 7.40 a.m.?

Ans :- 55 km.

2) A swimmer was swimming slowly from a beach to a small island, without resting. For every 10 m he swims, he is pushed back by the waves for 1m . It takes him 4 seconds to swim towards the island and 1 second to be pushed back by 1 m.
(a) How far would the swimmer have swum after 1 minute?
(b) What is the shortest time the swimmer would take to reach the island 505 m away?

Ans :- a) 108m
b) 4 min 39 sec

3) A large wheel makes 6 revolutions in 5 seconds while a small wheel makes 18 revolutions in 3 seconds.
(a) How many revolutions would the large wheel make in 8 minutes if it moves at a constant speed?
(b) If the large wheel makes 216 revolutions, how many revolutions will the small wheel make if both wheels start turning at the same time and move at a constant speed?

Ans :- a) Large wheel would make 576 revolutions
b) Small wheel will make 60 revolutions.

4) Perry Town and Phi City are 540 km apart. At 08 00, a lorry starts travelling to Phi City from Perry Town at a constant speed of 52 km/h. At 09 00, a car leaves Phi City for Perry Town at a constant speed of 72 km/h.
(a) At what time will the car and the lorry be 240 km apart?
(b) After leaving Phi City for 4 hours, the car increases its speed to 84 km/h. At what time would the car reach Perry Town?

Ans :- a) At 11 00
b) At 16 00 or 4.00 p.m.

5) Tony and Charles took part in a car race. Tony drove at a speed of 90 km/h. Both of them did not change their speed throughout the race. When Charles had covered 13 of the distance, Tony was 15 km in fromt of him. Tony reached the finishing line at 9.35 am. At what time did Charles reach the finishing line?

Ans :- At 10.05 am Charles reach the finishing line.

6) Wynn started her journey with 24.4ℓ of petrol in her car's tank. After travelling for a distance, she found that she had only 4.2ℓ of petrol left in the tank. She refilled $40 worth of petrol at $0.80 per litre. She continued her journey and at the end of it, she had 8.8ℓ of petrol left. If 0.2ℓ of petrol is needed for every 1 km, find the total distance Wynn covered for that day.

Ans :- Wynn covered 328 km on that day.

7) There are 2 teams of workers at a fast food restaurant. Team G has 30 more members than Team H. Each member in Team G prepares 4 burgers per minute while each member of Team H prepares 3 burgers per minute. In 1 hour, both teams prepare 36 600 burgers altogether. How many members are there in each team?

Ans :- Team G has 100 and Team H has 70 members.

8) Tap A takes 5 minutes to fill ¼ of a tank. Tap B takes 10 minutes to fill up the same tank to its brim. If both Taps A and B are turned simultaneously, how long will it take to fill the tank completely? (Leave your answer as a fraction in the simplest form)

Ans :- It will take 623 min .

9) Gary and Edwin started off together in the same direction from Town A and drove towards Town B at an average speed of 60 km/h and 96 km/h respectively. How far apart would they be after 20 minutes?

Ans :- They would be 12 km apart.

10) A car and a lorry which were 80 km apart started to travel towards each other at the same time. The car was 40 km/h faster than the lorry. They went past each other after 25 hours.
(a) How far did the lorry travel when it passed the car?
(b) Find the speed of the lorry.

Ans :- a) Lorry travelled 32 km
b) The speed of the lorry is 80 km/h.

11) Toy A and Toy B started from Point X and moved in the opposite direction round a circular track. Toy A took 6 minutes to reach Point X again at a speed of 10 m/min while Toy B was still 6 m away from Point X.
(a) What was the speed of Toy B?
(b) If both of them continued moving and stopped only after having moved 9 minutes from the starting time, how far apart would they be?

Ans :- a) 9m/min
b) 9m .