Please answer

[jalshri]

one day, nick started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his usual speed. How much time in minutes does nick usually take to reach his office from home?
a- 20
b-40
c-60
d-80
e-100

[jgabry]

Hi jalshri,

There are a few ways to solve this. Here's two different methods that work:

Method 1)
If D = distance to Nick's office, R = Nicks usual speed, and T = the usual # of minutes, then Nick's normal drive to work can be described using the standard distance, rate and time equation:

D = R*T

We can now modify this equation to incorporate the information we're given about this abnormal day.

D will be the same because the distance to his office hasn't changed. Regarding R, since he's going 25% slower, that means he's only going 75%, or 3/4, of his normal speed. We can write this as (3/4)R. And if he leaves 30 minutes late but arrives 50 minutes late, that means he is traveling for an extra 20 minutes. We can call this T + 20.

So now we have:

D = (3/4)R*(T +20)

Since both of our equations are equal to D, then they must be equal to each other. This will allow us to solve the problem:

R*T = (3/4)R*(T +20)
• dividing both sides by R:
T = (3/4)(T +20)
• multiplying both sides by 4, distributing the 3 on the right side:
4T = 3T + 60

T = 60 minutes

So Nick's normal time is 60 minutes.


Method 2)
Since he takes 20 minutes longer to get to work, we know that his slower time minus his normal time must equal 20.

So we can say SlowTime - NormalTime = 20 minutes

Using the D = R*T equation, we can see that T = D/R.

We can substitute this into our equation:

D/(75% of Normal Rate) - D/(NormalRate) = 20 minutes

D/(3/4)R - D/R = 20
•multiplying both sides by 3/4
D/R - (3/4)D/R = 15

(1/4)D/R = 15

D/R = 60

Since T = D/R, we again have that T = 60 minutes


Hope that helps!

[nareshchowdary28]

This can be achieved by using Manhattan's great RTD chart technique.

consider Nick's regular speed - 100mph (as they mentioned in the problem that speed variation is only in percentages, you can pick a smart number)
Usual time to reach office - t hrs

Today Nick's speed - 75mph (25% slow)
Today Nick's time - t+20 ( 50 mins late reach - 30 mins late start = total 20 mins extra time)

Chart is like below

R | T | D
--------------------
100 | t | d
---------------------
75 | t+20 | d
----------------------

now you have two equations to solve the problem

100 (t) = 75 (t+20) {as both are equal to d}

t = 60

Answer = 60

[tommywallach]

Great work with the explanations, guys! You don't even need me and Jen!

-t