please solve

Question

an accountant rides a bus part of the way to work everyday and walks the rest of the way. The bus averages 36 mph and the accountant walks at a speed of 3mph. The distance from home to work is 15mi and the total time of the trip is 2hrs. Find how far the accountant walks and how far he rides the bus.

 

How far he walks=

 

How far he rides the bus+

Answer 1

Let B = # hrs on Bus    and    Let W = # hrs walking

 

B + W = 2 since the total time is 2 hrs

 

Note that to find distance we use d = rt   for  distance = rate(time) so

the bus distance is (36 mph)(B) and the walking distance is (3 mph)(W) and they add to 15 miles so ...

36B + 3W = 15

 

We have two simultaneous equations that must both be true

 

B + W = 2

36B + 3W = 15

 

Let's use substitution to solve.  From the 1st equation we have B = 2 - W.  Put that in the 2nd equation:

 

36(2-W) + 3W = 15

72 - 36W + 3W = 15

-33W = -57

W = (-57)/(-33) = 57/33 = 19/11 hours or 1 8/11 hours that he walks

 

That means he rides the bus for 3/11 of an hour

 

To find the distance he rides the bus we take d = rt and get

 

d = (36 mph)(3/11 hr) = 108/11 miles = 9.82 miles

So he rides the bus for 9.82 miles

 

Since the total distance is 15 miles then he walks for 15 miles - 9.82 miles = 5.18 miles walking