City R and City S are 360 km apart. At 1.45 p.m., George is travelling at a uniform speed left City R for City S while Fred set off from City S to City R along the same road at a uniform speed, which was 12 km/h slower than that of George. The two met at 4.45 p.m.
- Find the speed of George.
- If Fred 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 George and Fred to travel from 1.45 p.m. to 4.45 p.m. = 3 h
Average speed of George and Fred
= 360 ÷ 3
= 120 km/h
George's speed
= (120 + 12) ÷ 2
= 132 ÷ 2
= 66 km/h
(b)
Fred's speed
= 66 - 12
= 54 km/h
Distance that Fred travelled in 3 h
= 3 x 54
= 162 km
Remaining distance that Fred needed to travel
= 360 - 162
= 198 km
Time that Fred needed to reach his destination after the two met
= 198 ÷ 54
= 3
3654 = 3
23 h
Answer(s): (a) 66 km/h; (b) 3
23 h