How long must a driver take to drive the final 70 miles of a trip if he wants to average 50 miles an hour for the entire trip and during the first part of the trip he drove 50 miles in $$1\frac{1}{2}$$ hours ?
Correct Answer: 54 min
Total distance = (57 + 50) miles = 120 miles
Average speed = 50 miles/hour
Required time of journey :
$$\eqalign{ & = \left( {\frac{{120}}{{50}}} \right){\text{ hr}} \cr & = \frac{{12}}{5}{\text{ hr}} \cr & = 2\frac{2}{5}{\text{ hr}} \cr & {\text{ = 2 hr }}24{\text{ min}} \cr} $$
Time taken to cover 50 miles :
$$\eqalign{ & = {\text{1}}\frac{1}{2}{\text{ hr}} \cr & = 1{\text{ hr 30 min}} \cr} $$
∴ Remaining time :
= (2 hr 24 min - 1 hr 30 min)
= 54 min
Average speed = 50 miles/hour
Required time of journey :
$$\eqalign{ & = \left( {\frac{{120}}{{50}}} \right){\text{ hr}} \cr & = \frac{{12}}{5}{\text{ hr}} \cr & = 2\frac{2}{5}{\text{ hr}} \cr & {\text{ = 2 hr }}24{\text{ min}} \cr} $$
Time taken to cover 50 miles :
$$\eqalign{ & = {\text{1}}\frac{1}{2}{\text{ hr}} \cr & = 1{\text{ hr 30 min}} \cr} $$
∴ Remaining time :
= (2 hr 24 min - 1 hr 30 min)
= 54 min