City K and City L are 432 km apart. At 3.48 p.m., Ken is travelling at a uniform speed left City K for City L while Pierre set off from City L to City K along the same road at a uniform speed, which was 12 km/h slower than that of Ken. The two met at 6.48 p.m.
- Find the speed of Ken.
- If Pierre 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 Ken and Pierre to travel from 3.48 p.m. to 6.48 p.m. = 3 h
Average speed of Ken and Pierre
= 432 ÷ 3
= 144 km/h
Ken's speed
= (144 + 12) ÷ 2
= 156 ÷ 2
= 78 km/h
(b)
Pierre's speed
= 78 - 12
= 66 km/h
Distance that Pierre travelled in 3 h
= 3 x 66
= 198 km
Remaining distance that Pierre needed to travel
= 432 - 198
= 234 km
Time that Pierre needed to reach his destination after the two met
= 234 ÷ 66
= 3
3666 = 3
611 h
Answer(s): (a) 78 km/h; (b) 3
611 h