Yuriko drove from Ashland to Bayville at an average rate of 40 miles

Question

Yuriko drove from Ashland to Bayville at an average rate of 40 miles per hour and from Bayville to Cabot at an average rate of 50 miles per hour. If Yuriko’s trip from Ashland to Bayville was 90 miles longer and took 3 hours more than her trip from Bayville to Cabot, how many hours did her trip from Ashland to Bayville take?

A. 5
B. 6
C. 7
D. 9
E. 10

A. 5
B. 6
C. 7
D. 9
E. 10

Diablobuster · Accepted Answer

A faster way to solve is:

distance = rate * time

(1) x = 50h 
(2) x + 90 = 40(h+3)

sub in x=50h into (2):

50h + 90 = 40h + 120
10h = 30
h = 3

Total time for location A to location B is h+3

total time = 3 + 3 = 6

gmatophobia · Answer

Let the distance between Bayville and Cabolt =  x

The distance between Ashland and Bayville =  x + 90

Time taken from Ashland to Bayville =  \frac{x+90 }{ 40}

Time taken from Bayville to Cabot =  \frac{x}{50}

\frac{x+90}{40} - \frac{x}{50} = 3

50x + 4500 - 40x = 6000

10x = 1500

x = 150

Distance from between Ashland and Bayville =  150 + 90 = 240

Speed between Ashland and Bayville = 40

Time taken =  \frac{240}{40} = 6  hours

Option B

JeffTargetTestPrep · Answer

From Bayville to Cabot:

distance = rate × time

distance = 50 × t

From Ashland to Bayville:

distance = 40 × (t + 3)

Since the trip from Ashland to Bayville was 90 miles longer than the trip from Bayville to Cabot, we have:

40(t + 3) = 50t + 90

40t + 120 = 50t + 90

30 = 10t

t = 3 hours

Therefore, the trip from Ashland to Bayville took:

t + 3 = 3 + 3 = 6 hours

Answer: B

Archit3110 · Answer

let B to C distance be x and time be t 
x+90 = 40 * ( t+3)
x=50*t
solve for t 
50t+90 = 90t +120
t = 3
t+3 ; 6 hrs
option B

DanTheGMATMan · Answer

Bread and butter distance problem:

https://www.youtube.com/watch?v=Y-1C-4JPfWc

whatsarc · Answer

A------40mph------B------50mph------C

A to B at every hour intervals at 40miles/hr
40,80,120,160,200, 240 
B to C at every hour intervals 50miles /hr
50,100, 150

When Yuriko drives A to B for 6 hours, she covers 240
And when she drives B to C for 3 hours, she covers 150.

Thats 90 miles difference and 3 hours difference.
 Thats the answer, 6hrs is what she travels for from A to B

Elite097 · Answer

Time ratio = 5:4 for a given distance x (between B to C)
Time taken to cover 90 miles= 90/40= 2.25 hours
Extra time taken to cover A to B compared to B to C= 3 hours 
Thus time to cover distance x between A to B= t+3-2.25= t+ 0.75
Thus 5:4= (t+0.75)/t. Solving for t=3 hours
Thus time taken to cover A to B = 3+3=6 hours

Yuriko drove from Ashland to Bayville at an average rate of 40 miles

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Yuriko drove from Ashland to Bayville at an average rate of 40 miles

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