City A and City B are 408 km apart. At 1.14 p.m., Zane is travelling at a uniform speed left City A for City B while Brandon set off from City B to City A along the same road at a uniform speed, which was 10 km/h slower than that of Zane. The two met at 4.14 p.m.
- Find the speed of Zane.
- 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 Zane and Brandon to travel from 1.14 p.m. to 4.14 p.m. = 3 h
Average speed of Zane and Brandon
= 408 ÷ 3
= 136 km/h
Zane's speed
= (136 + 10) ÷ 2
= 146 ÷ 2
= 73 km/h
(b)
Brandon's speed
= 73 - 10
= 63 km/h
Distance that Brandon travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Brandon needed to travel
= 408 - 189
= 219 km
Time that Brandon needed to reach his destination after the two met
= 219 ÷ 63
= 3
3063 = 3
1021 h
Answer(s): (a) 73 km/h; (b) 3
1021 h