Word Problem

[heshamelaziry]

While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

138

148

150

162

168

OA D

[papgust]

Lets take 2 eqns. with the assumption that
From A to B, it took x hours
From B to A, it took (5-x) hours

Distance, D1 = 115 * x ..... (1)
Distance, D2 = 135 * (5-x) ..... (2)

Equate both equations,

115x = 135 * (5-x)
x = 2.7 hours

Question is to find number of minutes it took from A to B (Which is x hours)
Convert 2.7 hours to minutes = 2.7 * 60 = 162 min.

Hence D.

[viju9162]

good way to solve .. thanks papgust....

I did a mistake taking in this form ..as Speed = distance/time.. therefore, time = distance/speed.

hence, 5 = x/115 + x/135

X is the distance of one side.. I was completly stuck here and couldn't proceed... How will you consider the unknown value ( x) here? Can you please let me know..

Thank you,
Viju

[papgust]

You were doing properly this way. I think you became impatient once you saw a big equation

You have this eqn,

5 = x/115 + x/135

Here x is primarily the same for this problem. You can simplify the eqn now,

5 = (135x + 115x)/(115 * 135)
250x = 77625
x = 310.5 (Common Distance)

Calculate the time taken separately,

310.5/115 = 2.7 hours
310.5/135 = 2.3 hours
------------
5 hours
------------

Question asks for time of A to B, so its 2.7 hours and convert it to min.


But, this approach takes a lot of time (Esp. while calculating x). This is the difference basically b/w the 2 approaches.

[viju9162]

ya i didn't proceed further looking at the big equation. Thank you

[heshamelaziry]

I got stuck exactly the same way viju9162 got stuck