Sarah and Jim leave a train station at the same time traveling 20mi/h faster that Jim’s train. After 3 hours the were 270 miles apart how fast was each train going

speed of Jim's train = 35 mi/h

speed of Sarah's train = 35 +20 mi/h = 55 mi/hour

Step-by-step explanation:

Let the speed of Jim's train be x mi/h

Given, Sarah and Jim leave a train station at the same time traveling 20mi/h faster that Jim’s train.

speed of Sarah's train = x + 20 mi/h

we know distance = speed * time

time = 3 hours

distance traveled by Sarah's train = 3*(x+20) = 3x+60 miles

distance traveled by Jim's train = 3*x =  3x miles

It is not given that if trains are moving in same or opposite direction.

if they are travelling in same direction

Then, then distance between them = total distance traveled by

faster train -  total distance traveled by

slower train = 3x +60 -3x = 60 miles

which is wrong as the two trains are 270 miles apart

hence, they are travelling in opposite direction

In this case

distance between them = total distance traveled by

faster train +  total distance traveled by

slower train = 3x +60 + 3x = 6x + 60 miles

given that the trains are 270 miles apart

6x + 60 miles = 270 miles

6x = 270 - 60 = 210

x = 210/6 = 35

Thus, speed of Jim's train = 35 mi/h

speed of Sarah's train = 35 +20 mi/h = 55 mi/hour