Question

Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.

A)1.8 hours
B)3.1 hours
C)2.7 hours
D)2.6 hours

Answer 1

so basically
D=RT
distance=rate times time

D=233
carlos speed=55
maria speed=50
total time=4.4 hours

so therefor we have to represent
carlos time
maria time
carlos distance
maria dstance

let's say that
remember that whatever carlost drove is 233 minus maria (time and distance)
and since we are solving for maria time and distnace, solve in terms of them
maria time=t
maria distance=d
carlos time=4.4-t
carlos distance=233-d

remember total D=RT
find their seperate equations
carlos
233-d=55(4.4-t)

maria
d=50(t)
use them to solve

233-d=55(4.4-t)
subsitute 50(t) for d
233-50t=55(4.4-t)
add 50t to both sides
233=55(4.4-t)+50t
distribute using distributiver protperty (a(b+c)=ab+ac)
55(4.4-t)=242-55t
233=242-55t+50t
add like terms
233=242-5t
add 5t to both sides
233+5t=242
subtract 233 from both sides
5t=9
divdie both sides by 5
t=1.8
maria drove 1.8 hours

the answer is A