word problem to help my daughter?

Question

During rush hour, Adriana can drive 20 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Adriana's rate on the side roads is 10 mi/h faster than her rate on the freeway, find her rate on the side roads.

Answer 1

I would use a proportion to solve this problem

(x = rate on freeway.....x + 10 = rate on side road)

20/ (x + 10) = 15/x

Cross multiply to get

20 x = 15 (x + 10)

Distribute the 15

20x = 15x + 150

Combine like terms

5x = 150

Solve for x

X= 30mi/h (rate on the freeway)

30mi/h + 10mi/h

= 40 mi/h

Answer 2

Let t be the time taken to travel 20 miles on the side roads or 15 miles on the freeway.

Then the freeway speed is 15/t, and the side road speed is 20/t.

Because the side road speed is 10 greater, you have

20/t = 15/t + 10.

Multiply both sides by t, and you get

20 = 15 + 10t

so 10t = 5, meaning t = 5/10 = 1/2. Therefore the side road speed is 20 / t = 20 / (1/2) = 20*2 = 40.

Answer 3

x = speed on the side roads
y = speed on the freeway.

Equations:
x = y + 10 (speed on side roads is 10 mph more than on freeway)
20/x = 15/y (same time traveling 20 miles on side road as 15 on freeway)

From the second equation, x = 4y/3. Substitute this into the first equation and we get
4y/3 = y + 10

So y=30 and x=40.

Freeway speed = 30 mph, or 15 miles in half an hour.
Side road speed = 40 mph, or 20 miles in half an hour.

Answer 4

Let x = the time it takes to travel
Rate on side roads RS=20/x
Rate on freeway RF=15/x

Rate on side roads = 10 + Rate on freeway
RS=10+RF
20/x = 10 + 15/x
multiply through by x
20 = 10x +15
10x = 5
x = 1/2 hours

RS = 20/(1/2) = 40 miles/hr
RF = 15/(1/2) = 30 miles/hr

Answer 5

She is driving at 40 miles per hour on the side roads and 30 miles per hour on the highway

It is about fractions
let
x = side road mph
y = highway mph

20 over 15 = x over y

we know that
x = y+10

so slove for y
20 over 15 = y+10 over y

Answer 6

Assuming its uniform velocity.Here time is same for both roads
t = time
x = speed on high way
x+10 = speed on side way


we have distance = speed * time
20 = speed(sideroads)*time --> 1 (this is for side roads)
20 = t(x+10) ------------- 1
and for High way with the same formula
15 = t*x -----------------2
divide 1 by 2
20/15 = ( x+10)/x
4x = 3x+30
x = 30
speed on high way = 30 miles/hr
speed on side roads = 30 + 10 = 40 miles /hr

answer 40 m/hr

Answer 7

35

Answer 8

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Answer 9

40mph