Verified answer

let x be the time spent in blizzard

25x+55(4-x)=200

25x+220-55x=200

x=2/3 hour

the other is 3 and 1/3 hour

Hi Tim.

Let B = the time traveled during the blizzard

Let T = the time traveled without the blizzard

With the information given, we can make two different equations:

B + T = 4 hours

(B)(25mph) + (T)(55mph) = 200 miles

If we solve the first equation for B, we get B = 4 - T

We can now substitute 4 - T for B in the second equation to get:

(4 - T)(25) + 55T = 200

Solving this equation for T gives us:

100 - 25T + 55T = 200

30T = 100

T = 3 1/3

Now plug the value of T (3 and 1/3) into the first equation to find B:

3 1/3 + B = 4

B = 2/3 of an hour

To find how far they drove in the blizzard, multiply 25 mph times 2/3 hour = 16 and 2/3 miles

Best wishes and good luck.

First, write the total distance as a sum of the two distances - d(1) is during the blizzard, and d(2) is for the rest of the trip. Let t(1) be the time it takes during the blizzard, and t(2) be the time for the rest of the trip.

Thus, we have 200miles = d(1) + d(2)

In each of the distances, distance is speed times time, so d(1) = 25mph*t(1) and d(2) = 55mph*t(2). Thus, 200miles = 25mph*t(1) + 55mph*t(2).

We also know that the total time, 4 hours, is the sum of the individual times, so 4hours = t(1) + t(2).

So, you have two equations.

200miles = 25mph*t(1) + 55 mph*t(2)

4hours = t(1) + t(2)

This is just a system of equations. Solve the second equation for t(1) and substitute into the first equation:

t(2) = 4 hours - t(1)

200miles = 25mph*t(1) + 55mph * (4hours - t(1))

Now that you only have one variable, solve.

200= 25*t(1) + 220 - 55*t(1)

-20 = -30*t(1)

t(1) = 2/3 hours

Now, substitute this value back into your second equation to solve for t(2), which is 3 1/3 hours.

So, they spent 2/3 hours (or 40 minutes) in the blizzard and 3 1/3 hours (or 3 hours and 20 minutes) driving.

t = time in blizzard

4-t = time not in blizzard

since distance = rate times time

distance in blizzard is 25t

other distance is 55(4-t) or 220-55t

25t + 220-55t =200

220-35t = 200

20=35t

t = 20/35 or 4/7 hours

distance is 25*4/7 or 100/7 = 14 2/7 miles

55 (4-4/7) = 55 * 24/7 = 185 5/7 miles

HINT: Write what you know in a table.

.................................. Distance ............... Rate ..................... Time

During blizzard ....... d ............................ 25 .......................... t

Rest of trip .............. 200 - d .................. 55 .......................... 4 - t

Total ........................ 200 ........................ ----- ........................ 4

Notice that the first two rows in the Distance and Time columns add up to the totals.

Remember that d = r * t. Apply this to your table.

.................................. Distance .......................... Rate ..................... Time

During blizzard ....... d = 25t ............................. 25 .......................... t

Rest of trip .............. 200 - d = 55(4 - t) ........... 55 .......................... 4 - t

Total ........................ 200 ................................... ----- ........................ 4

You have 2 equations.

d = 25t

200 - d = 55(4 - t)

Substitute d with 25t in the second equation.

200 - d = 55(4 - t)

200 - 25t = 55(4 - t)

Distribute the RHS.

200 - 25t = 55(4) + 55(-t)

200 - 25t = 220 - 55t

Add 55t to both sides.

200 - 25t + 55t = 220 - 55t + 55t

200 + 30t = 220

Subtract 200 from both sides.

200 + 30t - 200 = 220 - 200

30t = 20

Divide both sides by 30.

30t / 30 = 20 / 30

t = 2 / 3

Update your table.

.................................. Distance ...................... Rate ..................... Time

During blizzard ....... 25(2 / 3) ....................... 25 .......................... 2 / 3

Rest of trip .............. 55[4 - (2 / 3)] ............... 55 ......................... 4 - (2 / 3)

Total ........................ 200 ................................ ----- ....................... 4

.................................. Distance ............................ Rate ..................... Time

During blizzard ....... 16 2/3 ................................. 25 ......................... 2 / 3

Rest of trip .............. 55(10 / 3) = 183 1/3 .......... 55 ......................... 3 1/3

Total ........................ 200 ...................................... ----- ....................... 4

Convert 2 / 3 hours to minutes.

(2 / 3) hours * (60 minutes / hour) = 40 minutes

ANSWER: They spent 40 minutes in the blizzard and drove 16 2/3 miles in it.

25x + 55y = 200

x+y=4

do the rest