Question

Dale travels from city A to city B to city C and back to city A. Each city is exactly 120 miles from the other two. His average rate from city A to city B is 60 mph. His average rate from city B to city C is 40 mph. His average rate from city C to city A is 24 mph. What is Dale's average rate for the entire trip, in miles per hour?

Answer 1

Answer:

$average\ speed = 36\ mi/hr$

Step-by-step explanation:

Given:

Each city is exactly 120 miles from the other two.

Average rate from city A to city B = 60 mi/hr

Average rate from city B to city C = 40 mi/hr

Average rate from city c to city A = 24 mi/hr

We need to find the Dale's average rate for the entire trip.

Solution:

First we find the total time and total distance by following way.

Time taken to travel from A to B = $\frac{Distance}{Speed} = \frac{120}{60}= 2\ hr$

Time taken to travel from B to C = $\frac{Distance}{Speed} = \frac{120}{40}= 3\ hr$

Time taken to travel from C to A = $\frac{Distance}{Speed} = \frac{120}{24}= 5\ hr$

So, total time taken = $2+3+5=10\ hr$

Total distance =  120 + 120 + 120 = 360 miles

Using average speed formula.

$average\ speed = \frac{Total\ distance}{Total\ time\ taken}$

$average\ speed = \frac{360}{10}$

$average\ speed = 36\ mi/hr$

Therefore, the average rate for the entire trip $average\ speed = 36\ mi/hr$