City D and City E are 528 km apart. At 2.21 p.m., Ethan is travelling at a uniform speed left City D for City E while Fred set off from City E to City D along the same road at a uniform speed, which was 8 km/h slower than that of Ethan. The two met at 5.21 p.m.
- Find the speed of Ethan.
- If Fred 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 Fred to travel from 2.21 p.m. to 5.21 p.m. = 3 h
Average speed of Ethan and Fred
= 528 ÷ 3
= 176 km/h
Ethan's speed
= (176 + 8) ÷ 2
= 184 ÷ 2
= 92 km/h
(b)
Fred's speed
= 92 - 8
= 84 km/h
Distance that Fred travelled in 3 h
= 3 x 84
= 252 km
Remaining distance that Fred needed to travel
= 528 - 252
= 276 km
Time that Fred needed to reach his destination after the two met
= 276 ÷ 84
= 3
2484 = 3
27 h
Answer(s): (a) 92 km/h; (b) 3
27 h