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29 July, 01:59

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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  1. 29 July, 02:05
    0
    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
  2. 29 July, 02:07
    0
    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
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