word problem

Question

Joe and nancy decide to take a road trip. The first 64 miles of the drive is pretty easy, while the last 140 miles of the drive is filled with curves. They drove at an average of 7 miles per hour faster for the first 64 miles of the trip. The entire trip took 4 hours. How fast were joe and nancy driving for the first 64 miles of the trip

Answer 1

Le

Distance D = Rate X Time  You basically plug in what is known

D = 64+140 or a total of 204 miles  and T or time =4hours

R+7 = rate of first 64 miles  R = rate of last 140 miles

D=RT

204= 4(R+7) + 4R

204=4R + 28 + 4R  Now simplify

204-28=8R

176=8R  Divide both sides by 8

 

176/8=8R/8

R=22 that is the rate for the second 140 miles

R = 22  R+7=29 

The faster part is the 64 miles or R+7=29mph

 

 

 

 

Answer 2

distance=rate*time

d=rt

64=(r+7)(t)

140=(r)(4-t)

from the first equation you get (64/[r+7])=t

substitute into the second equation

140=(r)(4-[64/[r+7])

140=(r)([4r+28-64]/(r+7))

multiply both sides by r+7

140(r+7)=(r)(4r+28-64)

140r+980=(r)(4r-36)

140r+980=4r^2-36r

4r^2-36r-140r-980=0

4r^2-176r-980=0

divide both sides by 4

r^2-44r-245=0

245=5*7*7=5*(7*7)=5*49 and 49-5=44

factor

(r-49)(r+5)=0

r-49=0

r=49

64=(r+7)(t)

r+7=49+7

r=56 miles per hour

rate=56 mph for the first 64 miles of the trip (answer)