City V and City W are 378 km apart. At 4.45 p.m., Ethan is travelling at a uniform speed left City V for City W while Mark set off from City W to City V along the same road at a uniform speed, which was 12 km/h slower than that of Ethan. The two met at 7.45 p.m.
- Find the speed of Ethan.
- If Mark 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 Ethan and Mark to travel from 4.45 p.m. to 7.45 p.m. = 3 h
Average speed of Ethan and Mark
= 378 ÷ 3
= 126 km/h
Ethan's speed
= (126 + 12) ÷ 2
= 138 ÷ 2
= 69 km/h
(b)
Mark's speed
= 69 - 12
= 57 km/h
Distance that Mark travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Mark needed to travel
= 378 - 171
= 207 km
Time that Mark needed to reach his destination after the two met
= 207 ÷ 57
= 3
3657 = 3
1219 h
Answer(s): (a) 69 km/h; (b) 3
1219 h