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

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,