How do you set up this equation?

Question

on a road trip 5 friends drove at 60mph. on the way home they took the same route at 65mph how many miles did they drive on the way to california if the round trip tool 10 hours?

Answer 1

Its a system of equations.  

The first equation tells you that the two distances are equal.  If you travel 60 mph for x hours you go the same distance as if you travel 65mph for y hours.

The 2nd equation tells you that the total time is equal to 10 hours.

60x  = 65y  Ã¢Â‡Â’  60x - 65y = 0

x + y = 10

Solve this to get x = 10 - y

Substitute this in the first equation get

60x - 65y = 0

⇒ 60(10 - y) - 65y = 0

⇒ 600 - 60y - 65y = 0

⇒ 600 - 125y = 0

⇒ 600 = 125y

⇒ 600 / 125 = y

⇒ 4.8 = y

So sub. this in 2nd equation

x + y = 10

⇒ x + 4.8 = 10

⇒ x = 5.2

So he traveled 60 mph for 5.2 hours and 65mph for 4.8 hours

Thats a total of

60×5.2 + 6.5×4.8 = 624 miles

[That's 312 miles each way because 60×5.2 or 65×4.8 both equal 312]