Thomas and Tasha were hiking at a speed of 3.5 mph on their way back they were tired and their speed was 2mph. how long was the route if the way back took them 1 hour and 30 minutes longer?
Answers
Answer:
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 x Time
= 2(t+1.5) =
Since, length of the route is same both ways,Now substitute the value of t in the expression to get the distance of the route,
Distance = 3.5t
= 3.5 x 2
= 7 miles
Therefore, route was 7 miles long.
3.5t = 2(t+1.5)
3.5t = 2t + 3
3.5t - 2t = 3
1.5t = 3
t = 2 hours
hope it helps you in hw
Solution :-
Let us assume that, length of route us x miles .
So,
→ Distance covered in hiking = x miles
→ Hiking speed = 3.5 mph
then,
→ Time taken = Distance / speed = x/3.5 = (2x/7) hours .
Now,
→ Distance covered while coming back = x miles
→ New speed = 2 mph
then,
→ Time taken = Distance / speed = (x/2) hours .
A/q,
→ (x/2) - (2x/7) = 1 hours 30 minutes = 1(30/60) = 1(1/2) = 3/2 hours
→ (7x - 4x)/14 = 3/2
→ (3x/14) = (3/2)
→ 3x * 2 = 14 * 3
→ 6x = 42
→ x = 7 miles (Ans.)
Hence, Length of the route was 7 miles .
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