City F and City G are 342 km apart. At 5.51 p.m., Gabriel is travelling at a uniform speed left City F for City G while Ivan set off from City G to City F along the same road at a uniform speed, which was 9 km/h slower than that of Gabriel. The two met at 7.51 p.m.
- Find the speed of Gabriel.
- If Ivan 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 Gabriel and Ivan to travel from 5.51 p.m. to 7.51 p.m. = 2 h
Average speed of Gabriel and Ivan
= 342 ÷ 2
= 171 km/h
Gabriel's speed
= (171 + 9) ÷ 2
= 180 ÷ 2
= 90 km/h
(b)
Ivan's speed
= 90 - 9
= 81 km/h
Distance that Ivan travelled in 2 h
= 2 x 81
= 162 km
Remaining distance that Ivan needed to travel
= 342 - 162
= 180 km
Time that Ivan needed to reach his destination after the two met
= 180 ÷ 81
= 2
1881 = 2
29 h
Answer(s): (a) 90 km/h; (b) 2
29 h