City R and City S are 381 km apart. At 2.45 p.m., Asher is travelling at a uniform speed left City R for City S while Elijah set off from City S to City R along the same road at a uniform speed, which was 7 km/h slower than that of Asher. The two met at 5.45 p.m.
- Find the speed of Asher.
- If Elijah 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 Asher and Elijah to travel from 2.45 p.m. to 5.45 p.m. = 3 h
Average speed of Asher and Elijah
= 381 ÷ 3
= 127 km/h
Asher's speed
= (127 + 7) ÷ 2
= 134 ÷ 2
= 67 km/h
(b)
Elijah's speed
= 67 - 7
= 60 km/h
Distance that Elijah travelled in 3 h
= 3 x 60
= 180 km
Remaining distance that Elijah needed to travel
= 381 - 180
= 201 km
Time that Elijah needed to reach his destination after the two met
= 201 ÷ 60
= 3
2160 = 3
720 h
Answer(s): (a) 67 km/h; (b) 3
720 h