City X and City Y are 600 km apart. At 2.59 p.m., Rael is travelling at a uniform speed left City X for City Y while Gabriel set off from City Y to City X along the same road at a uniform speed, which was 10 km/h slower than that of Rael. The two met at 6.59 p.m.

1. Find the speed of Rael.
2. If Gabriel 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 Rael and Gabriel to travel from 2.59 p.m. to 6.59 p.m. = 4 h

Average speed of Rael and Gabriel
= 600 ÷ 4
= 150 km/h

Rael's speed
= (150 + 10) ÷ 2
= 160 ÷ 2 
= 80 km/h

(b)
Gabriel's speed
= 80 - 10
= 70 km/h

Distance that Gabriel travelled in 4 h
= 4 x 70
= 280 km

Remaining distance that Gabriel needed to travel
= 600 - 280
= 320 km

Time that Gabriel needed to reach his destination after the two met
= 320 ÷ 70
= 4⁴⁰₇₀
= 4⁴₇ h

Answer(s): (a) 80 km/h; (b) 4⁴₇ h