Word Problem: Determining Time

[baily106]

Hello,

This is from NOVA's math book.

It states: One day, Mr. Richards 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 Mr. Richards usually take to reach his office from home?

The answer choices are:
A) 20
B) 40
C) 60
D) 80
E) 100

Thanks.

[tommywallach]

Hey Baily,

Doesn't the NOVA book have explanations? I've never heard of them before, and I always get nervous around random books...

R * T = D
x y d
.75x y - 1/3 d

(The 1/3rd is because if you leave 30 mins late and arrive 50 minutes late, you only lost 20 minutes, which is 1/3 of an hour).

Set the two "equations" equal (because they both equal d)

xy = .75x(y - 1/3)
xy = .75xy - .25x
.25xy = .25x
.25y = .25
y = 1

1 hour is 60 minutes!

-t

[baily106]

As a representative of Manhattan Prep I can understand why you've never heard of NOVA. They did provide an explanation, but it wasn't clear to me.
Thanks.

[tommywallach]

Hey Baily,

Actually, it has nothing to do with being an MPrep person. I'm well acquainted with most of the major test-prep companies, so I get very nervous about people studying from books outside of those companies. There are so many good books from reputable sources available, there's really no need to use the obscure companies' materials. That doesn't mean they're bad, of course, but why take the risk? : )

-t