City Y and City Z are 584 km apart. At 1.46 p.m., Sam is travelling at a uniform speed left City Y for City Z while Jeremy set off from City Z to City Y along the same road at a uniform speed, which was 10 km/h slower than that of Sam. The two met at 5.46 p.m.
- Find the speed of Sam.
- If Jeremy 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 Sam and Jeremy to travel from 1.46 p.m. to 5.46 p.m. = 4 h
Average speed of Sam and Jeremy
= 584 ÷ 4
= 146 km/h
Sam's speed
= (146 + 10) ÷ 2
= 156 ÷ 2
= 78 km/h
(b)
Jeremy's speed
= 78 - 10
= 68 km/h
Distance that Jeremy travelled in 4 h
= 4 x 68
= 272 km
Remaining distance that Jeremy needed to travel
= 584 - 272
= 312 km
Time that Jeremy needed to reach his destination after the two met
= 312 ÷ 68
= 4
4068 = 4
1017 h
Answer(s): (a) 78 km/h; (b) 4
1017 h