Question

HELP PLEASE

2. A car is traveling on a small highway and is either going 55 miles per hour or 35 miles
per hour, depending on the speed limits, until it reaches its destination 200 miles
away. Letting x represent the amount of time in hours that the car is going 55 miles
per hour, and y being the time in hours that the car is going 35 miles per hour, an
equation describing the relationship is:
55x + 35y = 200

b. if the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour

c. if the car spends no time going 35 miles per hour, how long would the trip take? explain your reasoning

Answer 1

Answer: b.) 1 hour at 35 mph when the car spends 3 hours at 55mph

c.) The trip will take 3.64 hours which is about about 3 hours and 38 minutes if the car travels at 55mph the entire time.

(But it could take longer if the police stop the car to issue a ticket for going 55 mph in a 35mph zone!)

Explanation:

b.) 55(3) + 35y = 200 Multiply 55(3) = 165

165 + 35y = 200. Subtract 165 from both sides 200- 165 = 35

35y = 35 divide both sides by 35

y = 1, So the time traveling at 35mph is 1 hour

c.) 55x + 35y = 200

55x + 35(0) = 200 35×0 = 0

55x = 200 . Divide 200 miles by 55mph to find the time, x

200/55 = 3.63636 hours

To convert to minutes, multiply 60 × .63636 ≈ 38.18 minutes