Question

Mr. patterson takes his students in a fun train ride and plans to walk back and enjoy the beautiful countryside scenes. so, if the train goes 9 miles per hour and they can walk back 3 miles per hour the same way, how far could they ride if they need to be back in 4 hours?

1. dangkhoa
The total distance students ride from train is 9 miles.

### What is speed?

Speed is the pace that an object moves along a path in time, whereas velocity would be the rate & direction of movement. In other words, velocity is a vector, whereas speed is indeed a scalar value.
Te formula for speed is;
speed = distance/time
Now, according to the question
The total distance covered by train and by walk is same.
Let ‘d’ be the total distance covered.
The train goes 9 miles per hour;
Let ‘s1’ be the speed for the train.
And ‘t1’ be the time taken by the train to cover same distance ‘d’.
Thus, s1 = d/t1
9 = d/t1
or, d= 9t1
Now, speed of the students by walk is ‘s2’ = 3 miles per hour.
let ‘t2’ be the time taken by the students to cover the distance ‘d’.
s2  = d/t2
3 = d/t2
d = 3t2
Equate both distances;
9t1 = 3t2
3t1  = t2    (equation1)
The total time is 4 hours.
Thus, t1 + t2 = 4
t2  = 4 – t1
Substitute the value in equation 1.
3t1  = 4 – t1
4t1  = 4
t1 = 1 mile
Therefore, the total distance covered by the train is found to be 1 mile.
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