Question

The cross-country team left school and trotted to the duck pond at 3 mph. Then they ran back to the school at 7 mph. If the total trip took 10 hours, how far was it to the duck pond?

Answer 1

21 miles

Explanation:

Let's assume the distance from the school to the duck pond is "d" miles.

The time it took for the team to reach the duck pond at a speed of 3 mph is given by:

Time = Distance / Speed

Time = d / 3

The time it took for the team to run back to the school at a speed of 7 mph is given by:

Time = Distance / Speed

Time = d / 7

According to the given information, the total trip took 10 hours. Therefore, we can set up the equation:

Time to duck pond + Time back to school = 10

(d / 3) + (d / 7) = 10

To solve this equation, we can find a common denominator and simplify:

(7d + 3d) / 21 = 10

10d / 21 = 10

Now, we can cross-multiply and solve for "d":

10d = 10 * 21

10d = 210

d = 210 / 10

d = 21

Therefore, the distance from the school to the duck pond is 21 miles.