Problem Solving

hi all,
request to assist in solving the below problem:

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A) 30
B)45
C)60
D)75
E)It cannot be determined from the information given.

pappueshwar wrote:hi all,
request to assist in solving the below problem:

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A) 30
B)45
C)60
D)75
E)It cannot be determined from the information given.

This is the way I would solve this problem.

Let's assume that the distance between A& B is 180 miles (LCM of 60 and 90). This therefore means that the 1st half of the journey is equal to 90 miles. Similarly, the 2nd part of the journey will be equal to 90 miles.

We know that Speed = Distance/Time, implying that Time = Distance /Speed. From this formula, we can calculate the total time taken to travel from A to B. This is equal to: 180/60 = 3 hours
We can now calculate the time taken to travel the 1st half of the journey: 90/90 = 1 hour. This therefore means that he used 2 hours (3-1) to travel the 2nd half of the trip. Hence speed of the car in the second half of the trip = 90/2 = 45. Choose B
What's the OA?

HI,
yah ans is B

Ans is 45

Taking the distance as 60 miles-->30 in 1st half+30 in 2nd half .

equation in terms of time

30/90+t=60/60
t=2/3
v(avg speed of second half)=30/2/3=45mils/hr

pappueshwar wrote:hi all,
request to assist in solving the below problem:

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A) 30
B)45
C)60
D)75
E)It cannot be determined from the information given.

If we understand how rates work, we can determine the correct answer here just by examining the answer choices.

If the SAME distance is traveled at two different speeds, the average speed for the whole distance will be JUST A BIT LESS THAN THE AVERAGE OF THE TWO SPEEDS.

To illustrate:
60 miles traveled at 20 miles per hour will take 3 hours.
60 miles traveled at 30 miles per hour will take 2 hours.
Average speed for the whole trip = 120/5 = 24 miles per hour -- JUST A BIT LESS THAN THE AVERAGE of 20 and 30.

The reason is that it will take MORE TIME to travel the distance at the slower speed, so the average speed for the whole trip will be CLOSER to the slower speed.

In the problem above:
The faster speed is 90.
The average speed for the whole trip is 60.
Of the answer choices -- which represent the slower speed -- only 45 is viable, since 60 is just a bit less than the average of 45 and 90:
(45+90)/2 = 62.5.

The correct answer is B.