Solve Number Theory Problem to Find Time for Express Bus

[Marcelo Arevalo]

On a particular bus line, between Station A and Station J, there are 8 other
stations. Two types of buses, Express and Regular, are used. The speed of an
Express bus is 1.2 times that of a Regular bus. Regular buses stop at every
station, while Express buses stop only once. A bus stops for 3 minutes. On a
particular day, a Regular bus departed from Station A. 40 minutes later an
Express bus departed from the same station. The two buses arrived at
Station J at the same time. How long did the Express bus take from Station A
to Station J?

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As refer to answer key
the answer was 80
no idea how did they got it.

 

[MarkFL]

The time $t$ (in minutes) traveled by the regular bus (including stops) is:

\(\displaystyle t_R=\frac{d}{v}+24\)

And for the express bus (including the 40 minute delay) is:

\(\displaystyle t_E=\frac{10d}{12v}+40\)

Since they arrived at the last stop at the same time, you can equate the two times ($t_R=t_E$), and then solve for $d$, and then substitute for $d$ into either equation above to find $t$. What do you find?

 

[Marcelo Arevalo]

Is this the continuation of the given data above??
d/v + 24 = 10d/12v + 40
12d + 288v = 10d + 480v
2d = 480v -288v
d = 96vfrom 1 : tR = 96v/v + 24 = 120
from 2 : tE = 960v/12v + 40 = 120

 

[Marcelo Arevalo]

My solution:

please comment, thank you.

Regular Speed = Y
Express Speed = 1.2Y

Time taken if Regular = x/y + 8(3)/60 (min/hr)
if Express = x/1.2y + 3/60 (min/hr)

Combining the two equation:
we have; x/y + 24/60 = x/1.2y + 3/60 + 40/60
x/y + 24/60 = x/1.2y + 43/60
x/y - x/1.2y = 19/60 multiply both sides by 6y
6x - 5x = 114/60 y
x = 1.9y

Substituting on Express = x/1.2y + 3/60 mins
= 1.9y/1.2y + 3/60
= 98 mins or 1hr 38mins

 

[MarkFL]

Is this the continuation of the given data above??
d/v + 24 = 10d/12v + 40
12d + 288v = 10d + 480v
2d = 480v -288v
d = 96vfrom 1 : tR = 96v/v + 24 = 120
from 2 : tE = 960v/12v + 40 = 120

You have found the time it takes the regular bus...since the express bus left 40 minutes after the regular bus, you need to subtract 40 minutes to find the time it took the express bus.