City C and City D are 342 km apart. At 1.53 p.m., Jenson is travelling at a uniform speed left City C for City D while David set off from City D to City C along the same road at a uniform speed, which was 9 km/h slower than that of Jenson. The two met at 3.53 p.m.
- Find the speed of Jenson.
- If David continued to travel at the same speed, how long would it take for him to reach his destination after the two met? Express your answer in mixed number.
(a)
Time taken for Jenson and David to travel from 1.53 p.m. to 3.53 p.m. = 2 h
Average speed of Jenson and David
= 342 ÷ 2
= 171 km/h
Jenson's speed
= (171 + 9) ÷ 2
= 180 ÷ 2
= 90 km/h
(b)
David's speed
= 90 - 9
= 81 km/h
Distance that David travelled in 2 h
= 2 x 81
= 162 km
Remaining distance that David needed to travel
= 342 - 162
= 180 km
Time that David needed to reach his destination after the two met
= 180 ÷ 81
= 2
1881 = 2
29 h
Answer(s): (a) 90 km/h; (b) 2
29 h