City S and City T are 360 km apart. At 1.43 p.m., Mark is travelling at a uniform speed left City S for City T while Sam set off from City T to City S along the same road at a uniform speed, which was 12 km/h slower than that of Mark. The two met at 3.43 p.m.
- Find the speed of Mark.
- If Sam 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 Mark and Sam to travel from 1.43 p.m. to 3.43 p.m. = 2 h
Average speed of Mark and Sam
= 360 ÷ 2
= 180 km/h
Mark's speed
= (180 + 12) ÷ 2
= 192 ÷ 2
= 96 km/h
(b)
Sam's speed
= 96 - 12
= 84 km/h
Distance that Sam travelled in 2 h
= 2 x 84
= 168 km
Remaining distance that Sam needed to travel
= 360 - 168
= 192 km
Time that Sam needed to reach his destination after the two met
= 192 ÷ 84
= 2
2484 = 2
27 h
Answer(s): (a) 96 km/h; (b) 2
27 h