John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.
A) Tony: $3 \mathrm{mph}$; John: $6 \mathrm{mph}$
B) Tony: $\frac{5}{3} \mathrm{mph}$; John: $\frac{10}{3} \mathrm{mph}$
C) Tony: $\frac{3}{5} \mathrm{mph}$; John: $\frac{6}{5} \mathrm{mph}$
D) Cannot be determined without more information

Question

Quizplus · Accepted Answer

Let Tony's speed be $ x $ mph. Then John's speed is $ 2x $ mph. The time taken by Tony is $ \frac{10}{x} $ hours and by John is $ \frac{10}{2x} = \frac{5}{x} $ hours. Since John arrives 3 hours before Tony, we have $ \frac{10}{x} - \frac{5}{x} = 3 $. Solving this gives $ x = \frac{5}{3} $ mph for Tony and $ 2x = \frac{10}{3} $ mph for John.

John and Tony Start from Grays Lake at the Same 3mph3 \mathrm{mph}3mph

John and Tony Start from Grays Lake at the Same $3 \mathrm{mph}$