AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Q.

A is faster than B, A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then A’s speed is equal to.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

a

3km/hr

b

4km/hr

c

5km/hr

d

7 km/hr

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

Concept: Assigning variables for the speeds of A and B and the overall distance traveled allows us to begin addressing the problem. Using the relationship between speeds provided in the problem, we then determine the first equation. The relationship provided concerning times in the issue is then used to find our second equation utilizing the assumption that Time = distance/speed. To reach the desired outcome, we then solve both of the obtained equations.
We must ascertain A's speed.
Let's assume that A is moving at VA km/h and B is moving at VB km/h.
The answer to the question is that A is quicker than B.
⇒

V_{A} > V_{B}

Let x be the total number of steps they took.
The answer to the question is that x=24 km.
Given is that the combined speed of letters "A" and "B" is 7 km/hr.

V_{A} + V_{B} = 7 \frac{km}{hr}

V_{B} =

7-

V_{A}

distance = speed × time
Time taken by A =

\frac{24}{V_{A}}

Time taken by B =

\frac{24}{V_{B}}

The total amount of time they took, according to the question, was 14 hours.

\frac{24}{V_{A}} + \frac{24}{V_{B}} = 14

\frac{24 (7 - V_{A}) + 24 V_{A}}{(V_{A}) (7 - V_{A})} = 14

\frac{168 - 24 V_{A} + 24 V_{A}}{7 V_{A} - {V_{A}}^{2}} = 14

\frac{168}{14} = 14 (V_{A} - {V_{A}}^{2})

\frac{168}{14} = 7 V_{A} - {V_{A}}^{2}

12=

7 V_{A} - {V_{A}}^{2}

{V_{A}}^{2} - 7 V_{A} + 12 = 0

{V_{A}}^{2} - 4 V_{A} - 3 V_{A} + 12 = 0

V_{A} (V_{A} - 4) - 3 (V_{A} - 4) = 0

(V_{A} - 4) (V_{A} - 3)

=0

V_{A} = 3 km / hr

V_{A} = \frac{4 km}{hr}

V_{B} = (7 - 3) = 4 \frac{km}{hr}

V_{B} = (7 - 4) = 3 km / hr

V_{A} > V_{B}

V_{A} = 4 km / hr

and

V_{B} = 3 km / hr

Hence, option 2 is the correct answer.

Watch 3-min video & get full concept clarity

courses

No courses found

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

best study material, now at your finger tips!

live classes
progress tracking
24x7 mentored guidance
study plan analysis

download the app

gplay

mentor

Download the App

gplay

personalised 1:1 online tutoring