Question

Judith can ride her bike 2 mi/h faster than kelly. Judith takes 48 min less to travel 50 miles than Kelly does. What is each person's speed in miles per hour??

Answer 1

rate * time = distance

Let k = Kelly's speed or rate in miles/hour. Judith's rate is 2 greater or k+2.
Solving for time, time = distance/rate
Kelly's time = 50/k and Judith's time is 50/(k+2)
Kelly's time is 48 minutes or 48/60 hours more than Judith's. Have to keep the dimensional units consistent.
Equate the times adjusting for the time difference.
\[\frac{50}{k}-\frac{48}{60}\text{=}\frac{50}{k+2} \]Solve the equation for k.\[\left\{\left\{k\to -1-3 \sqrt{14}\right\},\left\{k\to -1+3 \sqrt{14}\right\}\right\} \]\[\{\{k\to -12.225\},\{k\to 10.225\}\} \]10.225 mph is Kelly's speed. Notice that the absolute value of the other solution for k is 2 greater than kelly's, so that must be Judith's speed, 12.225 mph. These two results are the requested answers for this problem.