Word problem about driving for 55mi/h to anther city, staying for 25hrs, and driving 45mi/h back. She is back 49 hours after leaving.

Question

Wilma drove at an average speed of 55 mi/h from her home in City A to visit her sister in City B. She stayed in City B 25 hours, and on the trip back averaged 45 mi/h. She returned home 49 hours after leaving. How many miles is City A from City B?

 

Thank you!

Answer 1

If Wilma stayed for 25 hours in City B, and her total time away from home was 49 hours, that means that she was traveling for 24 hours (49 - 25 = 24).  

 

The equation that ties together time, rate, and distance is 

 

Distance = Rate x Time

 

Let's define

 

t = the time it takes to get to her sister's house

 

then it follows that

 

24 - t = the time it takes to home home from her sister's house

 

(We don't know what t is yet, but we do know that the total travel time is 24.)

 

We can then use these variables in our distance equation

 

Distance = Rate x Time

 

On the way to her sister's:

 

Distance = 55 x t

 

On the way home from her sister's:

 

Distance = 45 x (24 - t) 

 

We assume that Wilma took the same route in both directions, so that the distance to her sister's house and the distance home will be equal to each other.  So, we can set the two expressions for distance equal to each other:

 

55t = 45 (24 - t)

 

Distribute to get

 

55t = 1080 - 45t

 

Collect t terms on one side:

 

100t = 1080

 

t = 10.8

 

Going back to our original variable definition, we see that t is the time that it took to get to her sister's.  We can then get:

 

10.8 hours to get to her sister's

24 - 10.8 = 13.2 hours to get home from her sister's

 

This still doesn't tell us how many miles it is from A to B.  We need to go back to the equation:

 

Distance = Rate x Time

 

To her sister's:

 

Distance = 55 mph x 10.8 hours = 594 miles

 

On the way home

 

Distance = 45 mph x 13.2 hours = 594 miles

 

 

 

Answer 2

Hi Elizabeth, 

 

When we talk about average speed the formula is:

 

X=V.T  we are trying to find X here.

 

 

She traveled total time of:

 

T=49-25= 24 hours

 

Going from A to B is the same distance from B to A.

 

Let's say time and speed from A to B are T1 and V1 respectively. 

 

T1= X/V1= X/55 hours

 

And time and speed from B to A are T2 and V2.

 

T2=X/T2= X/45 hours

 

Total time is:

 

T= T1+T2  hours

 

24= X/55 +X/45

 

Now we have one equation one unknown and we can solve it.

 

Best of luck! ;)

 

 

 

Answer 3

This isn't an answer. It's a guess. I'd say 600 miles. Since the 55 is an average and the 45 is an average, I surmised the average overall to be 50. She drove for 24 hours so at 50 mph I'd get a total distance of 1200 for the round trip and 600 for one way.

Answer 4

First subtract the 25 hours spent at her destination from the 49 hours away from home, for a total travel time of 24 hours 

 

Now this travel was portioned between the "to" leg and the "from" leg. For each, time = distance ÷ speed. Since the distance traveled is the same in both cases, and is the quantity requested, we'll call it x.

 

Thus, x/55 + x/45 = 24.

 

Solve by multiplying both sides of the equation by 45 • 55, then dividing by 100. (As a shortcut to avoid multiplying these big numbers, leave 24•45•55 in factored form, factor 100 and reduce)

Answer 5

Hours spent in driving = 49 - 25 = 24

 

If time required for one way = x hrs. time for other way = 24-x

 

45 x = 55 (24-x)

 

45x = 1320 - 55x

 

45x + 55x = 1320 

 

100 x = 1320

 

x = 13.2 hrs

 

Distance = 45 x 13.2 = 594 miles