City S and City T are 484 km apart. At 2.20 p.m., Archie is travelling at a uniform speed left City S for City T while Howard set off from City T to City S along the same road at a uniform speed, which was 9 km/h slower than that of Archie. The two met at 6.20 p.m.
- Find the speed of Archie.
- If Howard 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 Archie and Howard to travel from 2.20 p.m. to 6.20 p.m. = 4 h
Average speed of Archie and Howard
= 484 ÷ 4
= 121 km/h
Archie's speed
= (121 + 9) ÷ 2
= 130 ÷ 2
= 65 km/h
(b)
Howard's speed
= 65 - 9
= 56 km/h
Distance that Howard travelled in 4 h
= 4 x 56
= 224 km
Remaining distance that Howard needed to travel
= 484 - 224
= 260 km
Time that Howard needed to reach his destination after the two met
= 260 ÷ 56
= 4
3656 = 4
914 h
Answer(s): (a) 65 km/h; (b) 4
914 h