Help me determine the travel time for this word problem?

Question

On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Answer 1

Remember that Distance = Rate * Time, so Time = Distance/Rate

Let x be the speed on the final portion of the trip

4 = 200/(x + 20) + 80/x

Divide through by 4

1 = 50/(x+20) + 20/x

Multiply each side by (x+20)x

(x+20)(x) = 50x + 20(x+20)

x^2 + 20x = 70x + 400

x^2 - 50x - 400 = 0

Use the quadratic formula to find

x = (50 + 10*sqrt(41))/2

or

x = approx. 57.01562

Plug this value back into the problem

77 mph for 200 miles = approx. 1.4 hours

57 mph for 80 miles = approx. 2.6 hours

Added together = 4 hours

So the answer is that Sarah's car travelled approx. 77.016 mph for the first part of the trip

Answer 2

Ok..

Suppose the speed for the first part of the trip was x miles/hr

So the speed for the second part would b (x - 20) miles/hr

First part                                          

Speed x , Distance 200                    

Second Part

Speed (x - 20) , Distance 80

Average speed = (x + x -20) / 2 = (2x - 20) / 2 = 2 (x - 10) / 2 = x - 10

So for the total distance of 280 miles was done with the speed (x - 10) miles/hr

But the prob says that the total distance was done in 4 hrs.

So by the formula Speed = Distance / Time,

x - 10 = 280 / 4

x - 10 = 70

x = 70 + 10

x = 80

Now, just plug x = 80 into the first part of the prob which we already did..

So x = 80

Therefore the speed for the first part was 80 miles / hr

Answer 3

200

Answer 4

I'm not very good at math.  So I put this question on my watchlist to see how it is solved.  Image my surprise when I checked and there is 3 different solutions

1.  77 - 57

2.  70 - 50

3.  80 - 60

I would still like to see the answer.  Could you 3 look at your work again and see who is right?  Thank you

Answer 5

Trip #1 speed = s = S + 20

Trip #2 speed = S

First part of the trip the distance was 200 mi., and the second part of the trip it was 80 mi.

Using: d = rt

dist d = 280 mi.

time t = 4 hr

==> r (the rate) = d/t

==> S + 20 = 280/4

==> S = 50

So, the speed on the second part of the trip was 50 [mph].

The first part of the trip: s = S + 20 = 70 [mph]

Make sense?