From her house, Mary travels to New York at an average rate of 50 miles per

hour and then returns home at an average rate of 32 mph. After taking 2
hours longer on the return trip than the time it took her to get to New York,she finds that she still has 17 miles to go before she arrives home.

How many miles is it from New York to Mary’s house?

~Is there some kind of a equation to solve this problem or a method? Please help?

Distance=Rate/time

50(Time)=32(Time + 2 hours)+17
50 x t = 32t + 64 +17
50t = 32t +81
50t-32t=81
18t=81
t=4.5
Plug this in to the origional equation
50(4.5)= 225 miles to New York
Check answer
32(4.5 +2)+17=225
I hope this clears up this problem for you

Yes, there is a method to solve this problem using equations. Let's break it down step by step.

Let's assume the distance from Mary's house to New York is represented by "d" miles.

We know that Mary's average speed from her house to New York is 50 miles per hour. So, the time it takes her to travel from her house to New York is given by the equation:

Time1 = Distance / Rate1

Substituting the given values, we have:

Time1 = d / 50

Next, we are told that it takes Mary 2 hours longer on the return trip than the time it took her to get to New York. This can be represented as:

Time2 = Time1 + 2

We also know that Mary's average speed on the return trip is 32 miles per hour. So, the time it takes her to travel from New York to her house is:

Time2 = Distance / Rate2

Substituting the given values, we have:

Time2 = d / 32

Since we have two equations for Time1 and Time2, we can set them equal to each other and solve for "d":

d / 50 = d / 32 + 2

To solve this equation, we can multiply through by 50*32 to eliminate the fractions:

32d = 50d + 2*50*32

32d - 50d = 3200

-18d = 3200

d = -3200 / -18

d = 177.78 miles

Therefore, the distance from New York to Mary's house is approximately 177.78 miles.