Solve equation

Question

Mary drove from Amity to Belleville at a speed of 50mi/h. On the way back she drove at 60mi/h. The total trip took 4 2/5h of driving time. Find the distance beween these two cities.

Answer 1

Let Tab be the time to; Let Tba be the return time; Let Tttl be the total time: Tttl = Tab + Tba; Let d be the distance between the cities. 

 

Tab = d/50; Tba = d/60; redundantly, Tttl = Tab  +  Tba = d/50 + d/60  =  4.4 or 4 and 2/5.

 

The easiest common multiple of 50 and 60 is 300.

 

Multiply both sides of the equation Tttl = d/50 + d/60  =  4.4  by 300 to give

 

6d + 5d = 1320

 

11 d = 1320

 

d = 120

 

So the distance between the cities is 120 miles.

 

 

Answer 2

Speed*Time = Distance, so Time = Distance/Speed.  Let d = the distance between the towns.  The time to drive one way at 50 mph = d/50.  The time to drive back at 60 mph = d/60.

 

d/50 + d/60 = 4.4 hours

 

6d/300 + 5d/300 = 4.4

 

Solve for d.