City S and City T are 504 km apart. At 4.37 p.m., Daniel is travelling at a uniform speed left City S for City T while Reggie set off from City T to City S along the same road at a uniform speed, which was 12 km/h slower than that of Daniel. The two met at 7.37 p.m.

1. Find the speed of Daniel.
2. If Reggie 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 Daniel and Reggie to travel from 4.37 p.m. to 7.37 p.m. = 3 h

Average speed of Daniel and Reggie
= 504 ÷ 3
= 168 km/h

Daniel's speed
= (168 + 12) ÷ 2
= 180 ÷ 2 
= 90 km/h

(b)
Reggie's speed
= 90 - 12
= 78 km/h

Distance that Reggie travelled in 3 h
= 3 x 78
= 234 km

Remaining distance that Reggie needed to travel
= 504 - 234
= 270 km

Time that Reggie needed to reach his destination after the two met
= 270 ÷ 78
= 3³⁶₇₈
= 3⁶₁₃ h

Answer(s): (a) 90 km/h; (b) 3⁶₁₃ h