Problem Solving

[phoenix9801]

Using this formula D=R*T can someone please show me the most simplest way I can solve this hard problem. Please explain in the most simplest way possible and in details. Thanks

If you can show me how to solve both ways like backward solving, picking number, and algebraically I would greatly appreciate it.



If Dan has increased his average speed by 20 miles per hour, he would have decreased the time it took him to drive from his job to a certain restaurant by 25%. What was Dan's actual average speed, in miles per hour, when he drove from his job to the restaurant.

a) 30
b) 40
c) 45
d) 50
e) 60

[sam2304]

avg speed = s, given speed increased by 20 miles/hr so new speed = s+20
actual time = t, after change in speed new time = 0.75t
distance covered = D

Now both the distances are same only the speed and time changes.

d = speed * time

Since both the distances are equal, you can equate them

s*t = (s+20)*0.75t
st = 0.75st + 15t
0.25st = 15t
0.25s = 15
s = 60

IMO E.

[GMATGuruNY]

Using this formula D=R*T can someone please show me the most simplest way I can solve this hard problem. Please explain in the most simplest way possible and in details. Thanks

If you can show me how to solve both ways like backward solving, picking number, and algebraically I would greatly appreciate it.



If Dan has increased his average speed by 20 miles per hour, he would have decreased the time it took him to drive from his job to a certain restaurant by 25%. What was Dan's actual average speed, in miles per hour, when he drove from his job to the restaurant.

a) 30
b) 40
c) 45
d) 50
e) 60

He would have decreased the time it took him to drive from his job to a certain restaurant by 25%.
Time and rate are RECIPROCALS.
For the trip to take 3/4 of the actual time -- 1/4 less -- Dan would need to travel at 4/3 of his actual speed.
In other words, he would need to travel 1/3 faster than his actual speed.
Since the given increase in speed is 20mph, we get:
(1/3)r = 20
r = 60.

The correct answer is E.