► Speed and Distance sums
1) A man travels from City X to City Y at 4 km/h and from City Y to City X at 6km/h via the same route. The whole journey took 1 hour. Find the distance from City X to City Y.
Ans :- The distance is 2.4 km or 2 2⁄5.
2) At 1:15 p.m., Ann left Town X for Town Y, driving at a constant speed of 90 km/h throughout the journey. At 2.15 p.m., Ben left Town X and drove to Town Y at a certain speed. He maintained the same speed throughout his journey. At 4.15 p.m., both of them passed a Rest Point that was 135 km away from Town Y
(a) What time did Ann reach Town Y?
(b) Find Ben's speed throughout the journey.
Ans :- a) Ann reached Town Y at 5.45pm
b) Ben's speed was 135 km/h
3) The distance between Town X and Town Y was 875 km. Kenny started his journey from Town X to Town Y at an average speed of 70 km/h. After he had covered 3⁄5 of the journey, he decided to increase his speed so that he could reach Town Y one hour earlier. What was the increase in speed?
Ans :- Increase in speed is 17.5 km/h
4)Nancy started cycling from Point X to the library at 9 a.m. at a uniform speed of 500 m/min. At 9.10 a.m., Nancy passed Sam as he started cycling from Y towards the library at a certain uniform speed. At 9.20 a.m., Sam was 1 km ahead of Nancy. They continued cycling towards the library and Sam reached there at 9.37 a.m.
(a) What was Sam's speed? (Leave your answer in km/h)
(b) What was the distance from Point X to the library? (Leave your answer in km)
Ans :- a) Sam's speed was 36 km/h
b) The distance was 21.2 km.
5) John travelled from Town Q to Town R at an average speed of 72 km/h. He travelled 7⁄12 of the journey at an average speed of 70 km/h. After that, he decided to increase his speed to travel the remaining 450 km to Town R.
(a) Find John's speed in the last 450 km of the journey.
(b) If Kenny started his journey from Town R to Town Q at the same time as John at a constant speed of 90 km/h, how far would he have travelled before he met John?
Ans :- a) John's speed was 75 km/h
b) Kenny would have travelled 607.5 km.
6) Aunt Lily and Aunt Jane participated in a Walk-a-Jog for charity and started walking from the Community Club to the park at 07 30. Aunt Lily walked at an average speed of 75 m/min while Aunt Jane walked at an average speed of 50 m/min. When Aunt Lily reached the park and was walking back to the Community Club, she met Aunt Jane at 08 25 on her return journey. What was the distance between the Community Club and the park?
Ans :- The distance between the community club
and the park was 3437.5 m
7) Osman, Agnes and Hazel drove towards the airport in three different cars but they set off at the same time. Osman drove at an average speed of 100 km/h and reached the airport after 30 minutes. When Osman reached the airport, Hazel covered 7⁄10 of the journey while Agnes covered 3⁄5 of it. Hazel slowed down her driving speed for the rest of the journey as she wanted to reach the airport at the same time as Agnes. Find Hazel's speed in km/h for the last 3⁄10 of the journey.
Ans :- 45 km/h
8) Mr Phua drove from Town A to Town B. He took 2h to cover 3⁄4 of the journey at an average speed of 60 km/h. He covered the remaining journey at an average speed of 50 km/h. If he arrived at Town B at 12 noon, what time did he leave Town A?
Ans :- He left Town A at 9.12 a.m.
9) At 10:00 a.m., Mandy set off from Town X to Town Y at a constant speed of 70 km/h. At the same time, Nora drove off from Town Y to Town X.
After some time, they drove past each other. Later at 1 p.m., they were 40 km apart. Mandy reached Town Y at 3 p.m.
(a) How far from Town Y was Nora at 1 p.m.?
(b) What time did Nora reach Town X?
Ans :- a) 180 km
b) Nora arrived Town X at 3.50 p.m.
10) Sarah started driving from Town A to Town B at 4:30 a.m., travelling at a constant speed. James left Town A for Town B three hours after Sarah, travelling at a constant speed of 120 km/h. When James arrived at Town B, Sarah was still 160 km away from Town B and she reached Town B 2 hours later.
(a) Calculate the Sarah's average speed.
(b) What time did James overtake Sarah?
Ans :- a) Sarah's average speed is 80km/h
b) At 13 30 or 1.30pm James overtake Sarah
11) Two wheels with centres A and B are touching each other. Each wheel is of radius 7 cm. the wheels turn along the straight line XY in opposite directions as shown in Figure 1.
What is the distance between A and B when each wheel has made 5 complete turns? (Take π = 22⁄7 )
(The new position, not drawn to scale, is shown in Figure 2.)
Ans :- 454 cm.