Ski Trip Speed Word Problem

Question

Two families from the same neighborhood plan a ski trip.The first family is driving a newer vehicle and makes the 390-mike trip at a speed 5 mph faster than the second family. The second family takes a half-hour longer to make the trip. What are the speeds of the two families?

Answer 1

Ici, let's remember that distance = speed x time. Let's look at some possibilities for a product of 390.

 

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

 

Let's pick two pairs. 65(6) = 390. 60(6.5) = 390, so the two families travelled 65 and 60 mph.

 

 

 

 

 

 

 

 

Answer 2

I'm going to use F and S for the speeds of the first and second families.

 

390 = Ft = (S + 5)t = St + 5t

 

390 = S(t + 1/2) = St + S/2

 

Then setting these equal to each other we get that 

 

St + S/2 = St + 5t

 

S/2 = 5t

 

S = 10t

 

We have from the first equation that t = 390/F = 390/(S + 5)

 

S = 3900/(S + 5)

 

S(S + 5) = 3900

 

S² + 5S - 3900 = 0

 

(S - 60)(S + 65) = 0

 

So S = 60 and F = S + 5 = 65

 

And S = -65 and F = S + 5 = -60

 

We discard the negative solutions, because this doesn't make sense within the context of the problem.