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Maria normally spends half an hour driving to work. When her average speed is ten miles per hour slower than usual, the trip takes ten minutes longer. How many miles does she drive to work?

 Jul 15, 2015

Best Answer 

 #1
avatar+128053 
+10

Let R be her "normal" rate.....and R - 10 be her "reduced" rate......

 

And R*Time   = Distance......so......since the distances are equal.....we have.....

 

R(1/2)hr      =   (R - 10)(1/2  + 1/6) hr  .....  [10 min = 1/6 hr]

 

(1/2)R  =  (R -10)(2/3)

 

(1/2)R  =  (2/3)R - 20/3    rearrange

 

20/3  = (2/3 - 1/2)R

 

20/3  = (1/6)R     multiply both sides by 6

 

120/3   = R  = 40   and this is her normal rate in mph

 

And, her "reduced" rate is [40 - 10]   = 30 mph

 

And the distance to work is (1/2)h(40)m/h  = 20 miles

 

 

 Jul 16, 2015
 #1
avatar+128053 
+10
Best Answer

Let R be her "normal" rate.....and R - 10 be her "reduced" rate......

 

And R*Time   = Distance......so......since the distances are equal.....we have.....

 

R(1/2)hr      =   (R - 10)(1/2  + 1/6) hr  .....  [10 min = 1/6 hr]

 

(1/2)R  =  (R -10)(2/3)

 

(1/2)R  =  (2/3)R - 20/3    rearrange

 

20/3  = (2/3 - 1/2)R

 

20/3  = (1/6)R     multiply both sides by 6

 

120/3   = R  = 40   and this is her normal rate in mph

 

And, her "reduced" rate is [40 - 10]   = 30 mph

 

And the distance to work is (1/2)h(40)m/h  = 20 miles

 

 

CPhill Jul 16, 2015

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