City J and City K are 348 km apart. At 1.41 p.m., Simon is travelling at a uniform speed left City J for City K while Ryan set off from City K to City J along the same road at a uniform speed, which was 6 km/h slower than that of Simon. The two met at 3.41 p.m.
- Find the speed of Simon.
- If Ryan 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 Simon and Ryan to travel from 1.41 p.m. to 3.41 p.m. = 2 h
Average speed of Simon and Ryan
= 348 ÷ 2
= 174 km/h
Simon's speed
= (174 + 6) ÷ 2
= 180 ÷ 2
= 90 km/h
(b)
Ryan's speed
= 90 - 6
= 84 km/h
Distance that Ryan travelled in 2 h
= 2 x 84
= 168 km
Remaining distance that Ryan needed to travel
= 348 - 168
= 180 km
Time that Ryan needed to reach his destination after the two met
= 180 ÷ 84
= 2
1284 = 2
17 h
Answer(s): (a) 90 km/h; (b) 2
17 h