Problema Solution
sam and his mother drove 294 miles to the state fair. sam drove the farm truck at an average speed of 7 mph slower than his mother drove the family car. if same took an hour longer than his mother to get there, then what is sam's rate?
Answer provided by our tutors
let
v = Sam's rate, v>0
v + 7 = Sam's mother rate
d = 294 mi the distance each of the drove
t = the time of Sam's mother, t>o
t + 1 = the time of Sam
since speed(rate) = distance/time => distance = speed*time we have
v*(t + 1) = d
v*(t + 1) = 294
(v + 7)*t = d
(v + 7)*t = 294 divide both sides by (v + 7)
t = 294/(v + 7)
plug t = 294/(v + 7) into v*(t + 1) = 294
v*(294/(v + 7)+ 1) = 294
by solving we find
v = 42 mph
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Sam's rate is 42 mph.