Math Problem

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1

<p>Ms. Clark drove from her home to the museum at an average speed of 40 MPH and returned home with the same route traveling at and average speed of 35 MPH. If her total driving time was 2 hours how many minutes did it take ms clark to drive from her home to the museum?</p>

<p>Choices:
A)70 B)60 C)56 D) 45 E) 40
Could somebody provide me with a good explanation for the correct answer?
Help a fellow brother out, appreciate it very much.</p>

<p>Peace out
A Town
*music in background Denuh chi denuh, chi. denuh chi denuh chiii.</p>

2

<p>I’ll explain the best I can:</p>

<p>The crux of this problem is the formula d=rt. Now, d is the same for both trips (to and from) and r is given for both trips. We know that the 2 times added together equals 2 hours. So, here is what we know:</p>

<p>d1=d
d2=d
r1=40 MPH
r2=35 MPH
t1=t1
t2=2-t1</p>

<p>d=rt, so d=(40)t1=35(2-t1). Solve for t1:</p>

<p>(40)t1=70-35t1</p>

<p>t1=(70/75) hours= ((70*60)/75) minutes= <a href=“C”>b</a>56 minutes**</p>

<p>Note that t1 is paired with the rate of 40 MPH, which is the rate of house–>museum, so finding t1 was all that I needed to do. If the problem asked for the time it took from museum–>house, I would need to find t2, which is 120-56=64 minutes.</p>

3

<p>Ballparking this problem is way faster.

  1. Take the simple average of the speeds (40 + 35 = 75 /2 = 37.5)
  2. If speeds were equal for both ways (ie 37.5) , it would take her 60minutes (or half the time) to drive from home to the museum.
  3. Because she drove faster, it took her less time. Get rid of answers A & B.
  4. She only drove slightly faster, so it took her slightly less or 56 minutes.</p>
4

<p>^True. I eliminated A and B for sure when I first looked at the problem (because of reason 3 in MathMermaid’s post) and I felt that neither D nor E seemed plausible. Still, I would recommend you work out the problem unless you’re running out of time or if the answer choices were this:</p>

<p>A. 70
B. 60
C. 57
D. 56
E. 55</p>

<p>If C, D, and E were that close to each other, ballparking/guesstimating would not be advantageous at all.</p>