Question

Valerie set out to bicycle from the subway to the beach, a distance of 10 miles. After traveling a short while at 15 miles per hour, the bike developed a flat tire, and the trip had to be abandoned. The walk back to the subway station was made at a dejected 3 miles per hour. The entire episode took 48 minutes. At what distance from the subway did the flat tire occur?

A) 3 miles
B) 4 miles
C) 5 miles
D) 6 miles

Answer 1

The distance from the subway where Valerie experienced the flat tire is 4 miles, found by setting up an equation that includes the time spent cycling and the time spent walking, solving for the distance 'd'.

Step-by-step explanation:

The distance from the subway where the flat tire occurred can be calculated by first determining the time spent cycling and the time spent walking. Since the entire episode took 48 minutes (0.8 hours), we can say that the time spent cycling (tc) plus the time spent walking (tw) equals 0.8 hours.

We know Valerie cycled at 15 miles per hour and walked back at 3 miles per hour. If the flat tire happened at distance 'd', then she cycled for 'd/15' hours and walked back the same distance 'd' at 'd/3' hours. Adding these times together gives us the equation: d/15 + d/3 = 0.8.

By calculating this equation, multiplying every term by 15 to avoid fractions, we get 3d + 15d = 12. This simplifies to 18d = 12, resulting in d = 12/18, which simplifies further to d = 2/3 mile. As Valerie has traveled 2/3 of 15 miles per hour, this equates to 10 miles/hour. Hence, the correct answer to the distance from the subway when the flat tire occurred is option B, 4 miles.