To travel 38 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 48 miles riding a bicycle. Sue travels 7 miles per hour faster than Doreen. Find the times and rates of both girls.

Question

Quizplus · Accepted Answer

Let's denote Doreen's speed as $d$ mph. Therefore, Sue's speed is $d + 7$ mph. The time it takes for Doreen to travel 48 miles is $48/d$ hours, and the time it takes for Sue to travel 38 miles is $38/(d + 7)$ hours. According to the problem, Doreen takes 2 hours more than Sue, so we have the equation $48/d = 38/(d + 7) + 2$. Solving this equation for $d$ gives us Doreen's speed as 12 mph, which makes Sue's speed 19 mph. Plugging these speeds back into their respective distance/time equations gives us the times: Doreen travels for 4 hours (48 miles / 12 mph) and Sue travels for 2 hours (38 miles / 19 mph).

To Travel 38 Miles, It Takes Sue, Riding a Moped