PRECALC distance rate time word problem help

Question

A triathlete trains every morning. One of his training regiments involves cycling with a short run warm-up. He does a 3 mile run as a warm-up and then cycles for 40 miles. He monitors his pace and cycles 6 mph faster than he runs. If this training session lasts 3 hours, how fast does he run during his warm up?

a little confused with how to set it up, as every equation I make doesn't lead to an answer that makes sense.

Answer 1

Hi Gog:

Here's how to set up those pesky equations!

The important formula is: S = D/T where S = speed, D = distance, and T = time . . . . . . . . . . . eqn (1)

Let his running speed be x mph. Therefore, his cycling speed is 6x mph

Rearranging eqn(1), time he runs: T₁ = D/S = 3/x

and time he cycles: T₂ = 40/6x = 20/3x

But we know that T₁ + T₂ = 3 hours (his total raining time)

=> 3/x + 20/3x = 3

9/3x + 20/3x = 3 [getting to a common denominator of 3x

29/3x = 3

29 = 9x

x = 29/9

= 3.22 mph