Question

suppose that a trip from the dormitory to the lake at 30km/hour takes 12 minutes longer than the return trip at 48km/hour. How far apart are the dormitory and the lake?

Answer 1

Let distance be S. S=VT, where V=speed and T=time. T=S/V so V=30kph going to the lake, and T=T1=S/30.

T2, return time,=S/48. T1=T2+12/60 (we need to express 12 minutes as a fraction of an hour, because speed is km per hour). Therefore, S/30=S/48+1/5. S(1/30-1/48)=1/5; S(16/480-10/480)=1/5; S/80=1/5, S=80/5=16km.

CHECK

T1=(16/30)*60=(8/15)*60=32 minutes; T2=(16/48)*60=(1/3)*60=20 minutes. 32-20=12 minutes. OK.