Substitution story problem

Question

A boat can travel 100 mph more than 6 times the speed of a fish. If the boat can travel 1010 miles in the same amount of time the fish can travel 70 miles, how fast is each going?

Answer 1

Alright, Nicole, let's do this. I promise it's easier than you think. Remember that d = rt, so t = d/r. 

 

b = 6f + 100

1010/b = 70/f

 

Cross multiplying the 2nd equation, we get...

 

1010f = 70b

 

We already have b = 6f + 100, so we are going to substitute...

 

1010f = 70(6f + 100)

1010f = 420f + 7000

590f = 7000

f = 11.86 mph or 12 mph

 

b = 6(12) + 100 = 172 mph