Dan traveled to the lake and back. it took 3.5 hours less time to get there than it did to get back. the average speed on the trip there was 60 mph. the average speed on way back was 22.5 mph. how many hours did the trip there take?
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It took 7.7 hours for the trip for Dan

Solution:

Given, Dan traveled to the lake and back.  

It took 3.5 hours less time to get there than it did to get back.  

The average speed on the trip there was 60 mph.  

The average speed on way back was 22.5 mph.  

We have to find how many hours did the trip there take?

Let the time taken to reach lake be "t", then time taken to come back will be t + 3.5 hours.

Now, we know that, distance = speed x time taken

So, while travelling towards lake ⇒ distance = 60 x t

And while coming back ⇒ distance = 22.5 x (t + 3.5)

As the distance will be same, equate both the equations.

60t = 22.5(t + 3.5)

60t = 22.5t + 22.5 x 3.5

60t – 22.5t = 78.75

37.5t = 78.75

t = 2.1 hours

So, it took 2.1 hours to reach lake, then, it will take 2.1 + 3.5 = 5.6 hours to reach back.

Hence, the total time taken for the trip is 2.1 + 5.6 = 7.7 hours.