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 (in miles)

7 miles

Step-by-step explanation:

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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