Studdy AI Logo
Math

QuestionA truck driver is 150 miles from his exit, driving at 50 mph. Find his min and max driving hours before a rest stop within 30 miles.

Studdy Solution

STEP 1

Assumptions1. The truck driver is150 miles away from his planned exit. . He is traveling at a speed of50 miles per hour.
3. He plans to stop for a rest within30 miles of the exit on either side.

STEP 2

First, we need to find the minimum and maximum distances the truck driver will drive before stopping for a rest. The minimum distance is when he stops30 miles before the exit, and the maximum distance is when he stops30 miles after the exit.
Minimum distance=Total distance−Distance before exitMinimum\, distance = Total\, distance - Distance\, before\, exitMaximum distance=Total distance+Distance after exitMaximum\, distance = Total\, distance + Distance\, after\, exit

STEP 3

Now, plug in the given values for the total distance, distance before exit, and distance after exit to calculate the minimum and maximum distances.
Minimum distance=150 miles−30 milesMinimum\, distance =150\, miles -30\, milesMaximum distance=150 miles+30 milesMaximum\, distance =150\, miles +30\, miles

STEP 4

Calculate the minimum and maximum distances.
Minimum distance=150 miles−30 miles=120 milesMinimum\, distance =150\, miles -30\, miles =120\, milesMaximum distance=150 miles+30 miles=180 milesMaximum\, distance =150\, miles +30\, miles =180\, miles

STEP 5

Now that we have the minimum and maximum distances, we can find the minimum and maximum times the truck driver will drive before stopping for a rest. We can do this by dividing the distances by the speed.
Minimum time=Minimum distance/SpeedMinimum\, time = Minimum\, distance / SpeedMaximum time=Maximum distance/SpeedMaximum\, time = Maximum\, distance / Speed

STEP 6

Plug in the values for the minimum and maximum distances and the speed to calculate the minimum and maximum times.
Minimum time=120 miles/50 miles per hourMinimum\, time =120\, miles /50\, miles\, per\, hourMaximum time=180 miles/50 miles per hourMaximum\, time =180\, miles /50\, miles\, per\, hour

STEP 7

Calculate the minimum and maximum times.
Minimum time=120 miles/50 miles per hour=2.4 hoursMinimum\, time =120\, miles /50\, miles\, per\, hour =2.4\, hoursMaximum time=180 miles/50 miles per hour=3.6 hoursMaximum\, time =180\, miles /50\, miles\, per\, hour =3.6\, hoursThe truck driver will drive a minimum of2.4 hours and a maximum of3.6 hours before stopping for a rest.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord