The Santiago family went on an auto trip. They traveled a total of 15 hours to r

Question

The Santiago family went on an auto trip. They traveled a total of 15 hours to reach their destination. On the trip home, their average speed was 6 mph faster than on the trip going. They made the trip home in 1 and a half hours less time. What was the average speed for each part of the trip?
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This is all I got-

d=rt
Going= d1=rt
Returning= d2=(r+6)(t-1.5)
d1+d2= total distance
so d1=d2
rt= (r+6)(t-1.5)
rt=rt-1.5r+6t-9
But... how do I solve for r in terms of t and plug in 15 for t to get r for each part of the trip?

I am so confused..please help and give answer and explenation. Will rate asap!!!

Explanation / Answer

Total time taken = 15 hours
v1 = d/t1------> eqn 1
v2 = v1 + 6 = d/t2-------> eqn 2
t2 = t1-(3/2)
t1+t2=15
t1+t1-(3/2)=15
t1= 33/4
t2= t1-(3/2)= 27/4

Substituting in eqn 1 and 2
v1 x (33/4)= d
v2 x (27/4)= d
i.e. (v1 + 6)x (27/4)=d ===> (27/4)v1 - d = -(27/4) x 6 = -(81/2) -----> eqn 3
(33/4)v1 - d = 0 -------> eqn 4
Subtracting these eqns,
(6/4) x v1 = 81/2
v1 = (81/2) x (4/6) = 27
v2 = v1+6 = 33
v1 and v2 are the average speeds for each part of the trip

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