PSAT math question? ?

Question

Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent totally of one hour commuting to and from work, how many miles did Esther drive to work in the morning?

Answer 1

here...

let the distance from home to work be x. then

time taken for the 1st journey = x/45  

time taken for the 2nd =   x/30

total time taken = x/45 + x/30 = 1 h

so 2x/90  + 3x/90 = 1

5x / 90 = 1

5x = 90

x = 18 miles.

Answer 2

hr / 45mi * x + hr / 30 mi * x = 1 hr

where x = distance to work

Multiply by 90mi ; Divide by hr

2x + 3x = 90mi

5x = 90mi

x = 18mi

Answer 3

let the distance from home to work be x . Let time for going is t & time for returning is (1.5*t) or 1.5t.it is because the speed is 1.5 times less. now 2.5t = 1hr hence  t = .4hr . Hence the distance be (45*.4) or 18km.

Answer 4

r1 = 45 mph and t1 is time it takes to drive to work in the morning

r2=30 mph and t2 is time it takes to drive home in the evening

d = r * t (distance is rate times time)

t = 1 hour = t1+t2 thus t1 = t2 - 1

d = r1 * t1 = r2 * t2 = 45 t1 = 30 t2 = distance from work to home

plug in the eq for t1 (or t2)

45(t2-1) = 30t2 ... and solve for t2: 15/45 = 3/9

plug this into d = 30t2 = 90/9 = 10m