Atrain averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains. if a trip of 300 miles took 3 hour and 48 minutes, how much of it was through the mountains?

answer:

the answer to your question is time through the mountains = 47.73 min

step-by-step explanation:

data

speed plain = 90 mi/h

speed mountains = 37.5 mi/h

total time = 3 hr 48 min

process

1.- convert time to minutes

    3 hr 48 min = 228 min

2.- write equations for this problem

    total time = time through mountains (tm) ´time across the plains (tp)

    228 = tm + tp

solve for tm

  tm = tm = 228 - tp

3.- convert mi/h to mi/min

    90 mi/h = 1.5 mi/min

    37.5 mi/min = 0.62 mi/min

4.- write   equations for both stages

speed = distance / time

plains

    1.5 = x/tp

mountains

  0.62 = 300 - x / 228 - tp

5.- solve for x both equations

    x = 1.5tp

    141.36 - 0.62tp = 300 - x

6.- combine both equations to find tp

    141.36 - 0.62tp = 300 - 1.5 tp

    141.36 - 300 = 0.62tp - 1,5 tp    

    -158.64 = -0.88 tp

    tp = -158.64 / -0.88

    tp = 180.27

7.- find tm

    tm = 228 - 180.27

    tm = 47.73 min

87%

step-by-step explanation:

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