Pls help!!!!

Question

From point A to B, there is only uphill and downhill with no ground level. Mr Lim drives uphill at a speed of 20 km/h and downhill at a speed of 35 km/h. If he takes 4.5 hours to drive from point A to B and 3¾ hours from point B back to point A, what is the distance between the two points?

Answer 1

u=uphill distance, d=downhill distance. AB=u+d when going from A to B, and BA=d+u when returning, because downhill←→uphill when Mr Lim changes direction.

Distance=speed×time.

Time=distance/speed, 9/2=u/20+d/35; 15/4=d/20+u/35.

Multiply through by 140:

(1) 630=7u+4d; (2) 525=7d+4u.

4×(2) is 2100=28d+16u and 7×(1) is 4410=49u+28d=49u+2100-16u=2100+33u.

4410-2100=2310=33u, u=2310/33=210/3=70km.

So 4d=630-490=140, d=35km. AB=70+35=105km.