City D and City E are 312 km apart. At 1.25 p.m., Billy is travelling at a uniform speed left City D for City E while Brandon set off from City E to City D along the same road at a uniform speed, which was 12 km/h slower than that of Billy. The two met at 3.25 p.m.
- Find the speed of Billy.
- If Brandon 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 Billy and Brandon to travel from 1.25 p.m. to 3.25 p.m. = 2 h
Average speed of Billy and Brandon
= 312 ÷ 2
= 156 km/h
Billy's speed
= (156 + 12) ÷ 2
= 168 ÷ 2
= 84 km/h
(b)
Brandon's speed
= 84 - 12
= 72 km/h
Distance that Brandon travelled in 2 h
= 2 x 72
= 144 km
Remaining distance that Brandon needed to travel
= 312 - 144
= 168 km
Time that Brandon needed to reach his destination after the two met
= 168 ÷ 72
= 2
2472 = 2
13 h
Answer(s): (a) 84 km/h; (b) 2
13 h