City R and City S are 408 km apart. At 2.40 p.m., Eric 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 8 km/h slower than that of Eric. The two met at 5.40 p.m.
- Find the speed of Eric.
- 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 Eric and Elijah to travel from 2.40 p.m. to 5.40 p.m. = 3 h
Average speed of Eric and Elijah
= 408 ÷ 3
= 136 km/h
Eric's speed
= (136 + 8) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Elijah's speed
= 72 - 8
= 64 km/h
Distance that Elijah travelled in 3 h
= 3 x 64
= 192 km
Remaining distance that Elijah needed to travel
= 408 - 192
= 216 km
Time that Elijah needed to reach his destination after the two met
= 216 ÷ 64
= 3
2464 = 3
38 h
Answer(s): (a) 72 km/h; (b) 3
38 h