City S and City T are 378 km apart. At 4.44 p.m., Will is travelling at a uniform speed left City S for City T while Luke set off from City T to City S along the same road at a uniform speed, which was 12 km/h slower than that of Will. The two met at 7.44 p.m.
- Find the speed of Will.
- If Luke 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 Will and Luke to travel from 4.44 p.m. to 7.44 p.m. = 3 h
Average speed of Will and Luke
= 378 ÷ 3
= 126 km/h
Will's speed
= (126 + 12) ÷ 2
= 138 ÷ 2
= 69 km/h
(b)
Luke's speed
= 69 - 12
= 57 km/h
Distance that Luke travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Luke needed to travel
= 378 - 171
= 207 km
Time that Luke needed to reach his destination after the two met
= 207 ÷ 57
= 3
3657 = 3
1219 h
Answer(s): (a) 69 km/h; (b) 3
1219 h