Math word problem

Question

The Smith's took a camping trip. The campsite was 208 miles away. On the way home, they took the freeway and saved 45 minutes (3/4 of an hour) compared to the back roads trip there since they were able to average 12 mph faster. Find their average speeds and the time for each trip. 

 

How do I set this problem up and what are the average speeds and times?

Answer 1

208 miles

speed 12 mph faster on highway

average speeds and tmes?

d=rt= 208= xt = (x+12)(T)= (x+12)(t-3/4)

solve for x and t

then for x+12 and t-3/4 (in hours)

208= xt = (x+12)(t-3/4) t=208/x

208 = x(208/x) = (x+12)(208/x - 3/4)

multiply by 4

832 = (x+12)(832 -3x)

832x -3x^2 + 12(832) -36x = 832

3x^2 - 796x -11(832) =0

x = 796/6 +/-(1/6)sqr(796^2 + 12(11)(832)= about 796/6 +/- 862.23/6

= about 133 + 143.705 = 276.705 mph on back roads

x+12 = 288.705 mph for highway speed

t = 208/276.705 = about 3/4 hr = 45 minutes for back streets

T = 208/288.705 = about .702 hrs = about 42 minutes for highway time