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Tomas and Tasha were hiking at a speed of 3.5 mph. On their way back, they were tired and their speed was 2 mph. How long was the route if the way back took them 1 hour and 30 minutes longer?

Sagot :

Answer: Time: Approximately 2 hours and 21 minutes

Length: 6 miles

If this doesn't answer your question please read the explanation.

Step-by-step explanation:

1 hour and 30 minutes is 3/2 of an hour.

Therefore, we have them traveling at 2 mph for 3/2 hours.

distance = rate x time

2 mph * 3/2 = 3 miles.

3 * 2 = 6 miles.

time = distance/rate

Then there is 3.5 mph

3 miles/3.5 mph = 6/7 of an hour.

Adding them: 33/14 is reached (hours)

Approximately 2 hours and 21 minutes.

 To get the length of the route use the expression for speed,

Distance = Speed × Time

Length of the route is 7 miles.

It's given in the question,

 Speed of Tomas and Tasha initially = 3.5 mph

Therefore, distance travelled by both with the speed of 2 mph one way will be,

 Distance = 3.5t [Here, t = time ]

Speed of both while coming back = 2 mph

And the time taken = t + (1 hour 30 minutes)

                                 = (t + 1.5) hours

Therefore, distance travelled while coming back = Speed × Time

                                                                                  = 2(t + 1.5)

Since, length of the route is same both ways,

3.5t = 2(t + 1.5)

3.5t = 2t + 3

3.5t - 2t = 3

1.5t = 3

t = 2 hours

Now substitute the value of t in the expression to get the distance of the route,

Distance = 3.5t

               = 3.5 × 2

               = 7 miles

 Therefore, route was 7 miles long.

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