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Lily takes a train each day to work that averages 35 miles per hour . On her way home her train ride follows the same path and averages 45 miles per hour . If the total trip takes 2.5 hours , what equation can be used to find n, the number of miles Lilly's homes is for work

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altavistard

Answer:

49.2 miles

Step-by-step explanation:

The distance remains the same.                        d

The time spent on the outbound trip is t1 = -------------

                                                                         35 mph

and that on the inbound (return) trip is

                                                                              d

                                                                t2 = -------------

                                                                         45 mph

We combine these two fractions and set the sum = to 2.5 hours:

d(1/35 + 1/45) = 5/2

We wish to solve for d, the distance between home and work.

The LCD of 35, 45 and 2 is 630.

1/35 becomes 18/630; 1/45 becomes 14/630, and 5/2 becomes 1575/630.  Then we have the simpler equation   d(18 + 14) = 1575, or

d(32) = 1575, and d is then

d = 1575/32 = 49.2 miles

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