Book Maths Puzzle

A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph. The car traveled at an average speed of v
mph for the remaining part of the trip. The average speed for the entire trip was 50 mph.What is v in mph?

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Book Other Question

If Θ lies in 1st quadrant and cos Θ=8/17.
Then prove that,,

Cos(∏/6 + Θ) +cos(∏/4 –Θ) +cos(2∏/3) –Θ) =
{ (√3 – 1) / 2 + 1 / √2 } 23/17
An old man distributed all the coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 36 times the difference between the two numbers. How many coins did the old man have?