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# Traveling at a constant rate of 15 miles per hour, it took Bob x hours

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Math Expert
Joined: 02 Sep 2009
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Traveling at a constant rate of 15 miles per hour, it took Bob x hours  [#permalink]

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24 Jan 2019, 03:05
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:07) correct 15% (00:56) wrong based on 51 sessions

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Traveling at a constant rate of 15 miles per hour, it took Bob x hours to go from his home to his school. Traveling at a constant rate of 20 miles per hour, it took Bob x − 1 hours to travel the same route. What is the value of x?

A 2
B 3
C 4
D 5
E 6

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Traveling at a constant rate of 15 miles per hour, it took Bob x hours  [#permalink]

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24 Jan 2019, 03:11
Bunuel wrote:
Traveling at a constant rate of 15 miles per hour, it took Bob x hours to go from his home to his school. Traveling at a constant rate of 20 miles per hour, it took Bob x − 1 hours to travel the same route. What is the value of x?

A 2
B 3
C 4
D 5
E 6

15x = 20(x-1)

15x = 20x -20

x = 4.

*** Distance = time * speed.
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Posts: 2597
Re: Traveling at a constant rate of 15 miles per hour, it took Bob x hours  [#permalink]

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24 Jan 2019, 04:30

Solution

Given:
• $$s_1 = 15$$ miles per hour, and $$t_1 = x$$ hours
• $$s_2 = 20$$ miles per hour, and $$t_2 = x – 1$$ hours
• Both distances are same

To find:
• The value of x

Approach and Working:
We know that distance = speed * time
• Implies, $$s_1 * t_1 = s_2 * t_2$$
• Thus, 15x = 20(x - 1)

Therefore, $$x = \frac{20}{5} = 4$$

Hence, the correct answer is Option C

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Re: Traveling at a constant rate of 15 miles per hour, it took Bob x hours  [#permalink]

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24 Jan 2019, 05:07
Bunuel wrote:
Traveling at a constant rate of 15 miles per hour, it took Bob x hours to go from his home to his school. Traveling at a constant rate of 20 miles per hour, it took Bob x − 1 hours to travel the same route. What is the value of x?

A 2
B 3
C 4
D 5
E 6

Using logic, we know that in second case, Bob travelled 1 hr less because he travelled 5 miles extra for each of the (x - 1) hrs. This is the distance he would have covered in the last hour in the first case.

5*(x - 1) = 15
x = 4

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Re: Traveling at a constant rate of 15 miles per hour, it took Bob x hours  [#permalink]

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24 Jan 2019, 07:07
Bunuel wrote:
Traveling at a constant rate of 15 miles per hour, it took Bob x hours to go from his home to his school. Traveling at a constant rate of 20 miles per hour, it took Bob x − 1 hours to travel the same route. What is the value of x?

A 2
B 3
C 4
D 5
E 6

Let the distance travelled be 60 miles (LCM of 15 & 20)

So, Travelling at 15 miles/hour time taken is 4 hours & Travelling at 20 miles/hour time taken is 3 hours

Thus, the value of x is 4, Answer must be (C) 4
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Joined: 15 Feb 2018
Posts: 247
Re: Traveling at a constant rate of 15 miles per hour, it took Bob x hours  [#permalink]

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27 Jan 2019, 19:58
When I first saw these types of questions I could answer the simple ones, but was still confused by the units. I'm putting the below for others in similar situations.

1st trip $$\frac{15(miles)}{1(hour)}·x(hours)=distance$$

2nd trip $$\frac{20(miles)}{1(hour)}·(x-1)(hours)=distance$$

The distance is the same in both so we can have the equations equal each other

$$\frac{15(miles)}{1(hour)}·x(hours)=\frac{20(miles)}{1(hour)}·(x-1)(hours)$$

Simplification: Each side has hours in the denominator and numerator so they can be cancelled from each side. Just remember that we're trying to find x and it uses the unit hours

$$\frac{15(miles)}{1}·x=\frac{20(miles)}{1}·(x-1)$$

Simplification: Both sides of the equation use the unit miles, so it can be cancelled from both sides of the equation.

$$\frac{15}{1}·x=\frac{20}{1}·(x-1)$$

15x=20x-20
0=5x-20
0=x-4
4=x
Re: Traveling at a constant rate of 15 miles per hour, it took Bob x hours   [#permalink] 27 Jan 2019, 19:58
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