Question

It takes Mike 1 hour to get to work each day. He first rides the train, which travels at an average rate of 65 miles per hour. Then he rides the subway train, which travels at an average rate of 25 miles per hour. If the total distance that he travels from home to work is 61 miles, how many minutes does Mike spend riding the subway each morning?

its has to be in minutes

Answer 1

Time_subway = 6 minutes

Explanation:

Total time to get to work = 1 hour

Total_distance = 61 miles

Speed_train = 65 miles/h

Speed_subway = 25 miles/h

The fomula for speed is defined as

Speed = distance/ time, which means that

Time = distance/speed

Total_time = time_train + time_subway

Total_time = (distance_train/Speed_train) +

(distance_subway/Speed_subway )

1h = (distance_train/65) + (distance_subway/25 )

We also know that

Total_distance = 61 miles = distance_train + distance_subway

We solve the system of two equations

1 = (distance_train/65) + (distance_subway/25 )

61 = distance_train + distance_subway

We obtain that

distance_train = 58.5 miles

distance_subway = 2.5 miles

So the time spent on the subway is

t_sub = (2.5 mi/25 mi/h) = 0.1 h

0.1 h is equal to 6 minutes

Answer 2

Mike spends 6 minutes riding

Explanation:

Let x be the amount of time spent in train and y be the amount of time spent in subway (in hours).

x + y = 1

65x + 25y = 61

Rearranging equation 1:

x = y - 1

Substituting equation 3 in equation 2

65(1 - y) + 25y = 61

65 - 65y + 25y = 61

4 = 40y

y = 0.1 hours

Converting hours to minutes:

0.1 x 60 = 6 minutes

Mike spends 6 minutes riding the subway.