Question: I travel the first part of my journey at 40 miles per hour and the second part at 60 miles per hour and cover the total distance of 240 miles to my destination in 5 hours. How long did the first part of my journey last?

1. 4 hours
2. 2 hours
3. 3 hours
4. 2.5 hours
5. 5 hours

Correct Answer: (C)

Solutions and Explanation

Approach Solution 1 :

Use weighted averages since time taken determines the weights when averaging speed.

The two speeds are 40 mph and 60 mph, with an average speed of 48 mph calculated from 240/5.

w1/w2 = (60 - 48)/(48 = 40) = 3/2

Therefore, the first portion of the journey took 3/5 of the total time. This is actually 3 hours.

Approach Solution 2 :

Consider the time taken for 1st part as t

Now we get time taken for 2nd part = 5 - t

The total distance is the value of sum of D1 and D2

=> 240 = 40*t + 60*(5 - t)
=> 240 = 40t + 300 - 60t
=> 240 = 300 - 20t
=> 20t = 300 - 240 = 60
=> t = 3 hours

As a result, 3 hours is the time taken for the first part of the journey.

Approach Solution 3 :

We know that the, total distance is 240 miles and total time is 5 hours

Let us write the equations from the given information.

Equation - (1) is 240 = 5x (where x is the average speed)
Equation - (2) is 240 = 40t1 + 60t2
Equation - (3) is 5 = t1+t2

Let us solve for x,

=> 240 = 5x
=> x = 240/5
=> x = 48

Now combine equations all the equations:

From equations (1) and (2),
We get 5x = 40t1 + 60t2

Replace 5 from the third equation
=> 48(t1+t2) = 40t1 + 60t2

By using ratio method,

we get t1:t2
=> 60-48 : 48-40
=>12:8
=> 3:2

Now we have t1 as 3 and t2 as 2.
For verification, t1+t2 = 5
240 = 40(3) + 60(2) = 120 + 120 = 240

Therefore 3 hours is the time taken for the first part.

“I travel the first part of my journey at 40 miles per hour” - is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

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