A driver of a car took a day trip around the coastline driving at two different speeds. He drove 7070 miles at a slower speed and 200200 miles at a speed 3030 miles per hour faster. If the time spent driving at the faster speed was twicetwice that spent driving at the slower speed, find the two speeds during the trip.

Question

Physics

Haven Buchanan

21 October, 12:38

A driver of a car took a day trip around the coastline driving at two different speeds. He drove 7070 miles at a slower speed and 200200 miles at a speed 3030 miles per hour faster. If the time spent driving at the faster speed was twicetwice that spent driving at the slower speed, find the two speeds during the trip.

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Answers (2)

Know the Answer?

Mina Nolan · Answer 1

complete question:

A driver of a car took a day trip around the coastline driving at two different speeds. He drove 70 miles at a slower speed and 200 miles at a speed 30 miles per hour faster. If the time spent driving at the faster speed was twice that spent driving at the slower speed, find the two speeds during the trip.

Answer:

slower speed

speed = 70 miles/hr

Faster speed

speed = 100 miles/hr

Explanation:

The driver took a day trip at two different speed. The first speed was slower while the second was faster.

let the speed be divided into 2

Slower speed

speed = a

distance = 70

speed = distance/time

time = distance/speed

time = 70/a

Faster speed

speed = a + 30

distance = 200

speed = distance/time

time = distance/speed

time = 200/a + 30

Since the faster speed time is twice the slower speed time it can be represented as follows:

2 * 70/a = 200/a + 30

140/a = 200 / a + 30

cross multiply

140a + 140 (30) = 200a

4200 = 200a - 140a

4200 = 60a

divide both sides by 60

4200/60 = a

a = 70

Inserting the value of a in the time of the faster speed formula

time = 200/a + 30

time = 200/100

time = 2 hr

slower speed

speed = distance/time

speed = 70/1

speed = 70 miles/hr

Faster speed

speed = distance/time

speed = 200/2

speed = 100 miles/hr

Javier Weeks · Answer 2

Slower speed = 70 mph

Faster speed = 100 mph

Explanation:

Let the slower speed be x miles per hour

Then, the faster speed = (x+30) miles per hour

Let the time spent driving at the slower speed (that is, at x mph) = t

Then, time spent driving at the faster speed (that is, at (x+30) mph) = 2t

speed = (distance) / (time)

Distance = speed * time

Distance covered during the slower speed = x * t = xt = 70 (given in the question)

xt = 70 (eqn 1)

At the faster speed

Distance covered = (x+30) (2t) = 2t (x+30)

Distance covered during faster speed = 200 miles

2t (x+30) = 200

2xt + 60t = 200

Recall (eqn 1)

xt = 70

2 (70) + 60t = 200

60t = 60

t = 1 hour.

xt = 70

Slower speed = x = 70 mph

Faster speed = (x+30) = 100 mph