Question

Stanley practices his running, swimming, and biking every day. During these practices, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?

a) What distance did Stanley cover while running?
Option 1: 10 miles
Option 2: 15 miles
Option 3: 20 miles
Option 4: 25 miles

b) What distance did Stanley cover while biking?
Option 1: 16 miles
Option 2: 20 miles
Option 3: 24 miles
Option 4: 32 miles

Answer 1

Stanley ran for a distance of approximately 15 miles and biked for about 32 miles, after determining the time he spent on each activity and multiplying by his respective speeds.

Step-by-step explanation:

Let's denote the time spent swimming by t hours. Since Stanley ran for half an hour longer than he swam, his running time was t + 0.5 hours. Given that his biking time was twice his running time, it would be 2(t + 0.5) hours.

Using the speeds provided, we can now determine the distances covered during each activity:

• Running distance = 9 mph * (t + 0.5) hours
• Swimming distance = 2.5 mph * t hours
• Biking distance = 16 mph * 2(t + 0.5) hours

Total distance = Running distance + Swimming distance + Biking distance

64 miles = 9(t + 0.5) + 2.5t + 16×2(t + 0.5)

Solving this equation for t gives:

64 = 9.5t + 4.5 + 32t + 16

64 = 41.5t + 20.5

t = 1.05 hours (Swimming time)

Running time = 1.05 + 0.5 = 1.55 hours

Biking time = 2×1.55 = 3.1 hours

Now, we can find out the distances covered:

• Running distance = 9 mph × 1.55 hours = 13.95 miles, so Option 2: 15 miles (rounding to the nearest mile)
• Biking distance = 16 mph × 3.1 hours = 49.6 miles, so Option 4: 32 miles (rounding to the nearest mile)