City S and City T are 456 km apart. At 4.57 p.m., Jack is travelling at a uniform speed left City S for City T while Cole set off from City T to City S along the same road at a uniform speed, which was 10 km/h slower than that of Jack. The two met at 8.57 p.m.
- Find the speed of Jack.
- If Cole 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 Jack and Cole to travel from 4.57 p.m. to 8.57 p.m. = 4 h
Average speed of Jack and Cole
= 456 ÷ 4
= 114 km/h
Jack's speed
= (114 + 10) ÷ 2
= 124 ÷ 2
= 62 km/h
(b)
Cole's speed
= 62 - 10
= 52 km/h
Distance that Cole travelled in 4 h
= 4 x 52
= 208 km
Remaining distance that Cole needed to travel
= 456 - 208
= 248 km
Time that Cole needed to reach his destination after the two met
= 248 ÷ 52
= 4
4052 = 4
1013 h
Answer(s): (a) 62 km/h; (b) 4
1013 h