Question

a motor boat travelling at 18 miles per hour travelled the length of a lake in one-quarter of an hour less time than it took when travelling at 12 miles per hour. what was the length in miles of the lake?

Answer 1

Let the length of the lake be d miles and let the time to travel d miles at 12 mph be t hours.
Now we can form two equations:
\[\large t=\frac{d}{12}\ ...............(1)\]
\[\large t-\frac{1}{4}=\frac{d}{18}\ ...........(2)\]
If we now plug the value of t from equation (1) into equation (2) we get
\[\large \frac{d}{12}-\frac{1}{4}=\frac{d}{18}\ ...........(3)\]
Now you need to solve equation (3) to find the value of d.