# Time and Speed Puzzle

Raja’s office is 9 km from his home. One day, he decided to jog to work in order to increase his fitness. He estimates the journey time to be a little over 1 hour 45 minutes.

At first he feels fine, but before long his energy beings to fade and he realizes he will not be able to run the whole distance. A passing taxi is the answer to his prayer. Raja hails the cab and completes his journey, arriving at work one hour 10 minutes earlier than he had anticipated.

Assuming Raja could at 1/6 the speed of the cab, how far did he run before he hailed the taxi?

#### Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

## 10 thoughts to “Time and Speed Puzzle”

1. Thanks Guys for the interesting discussion 🙂

We agree with Ashish Kumar’s explanation. Poor Raja could only manage to run 1.8 Km before he had to hail the taxi.

@Mohit: Suggestion well appreciated. Now onwards for dicey questions like this we will provide you the options.

2. Ashish Kumar says:

yeah u r rite.i was also the victim of not having read dat “a little over” phrase

3. Mohit says:

Frankly put, for such questions, you need 4 options 🙂

A) 2 KM
B) 1.8 KM
C) 8 KM
D) 2.5 KM

Usually in CAT they put such questions to create confusion, as many people do not read between lines. And you have to choose the best answer.

4. Ashish Kumar says:

then this question does not have an unique answer. his jogging speed could well be 4.9 kph b’coz “a little” can not be quantified.

5. Ashish Kumar says:

how exactly did u then calculate???

6. Mohit says:

“a little over” 1 hour 45 minutes to travel 9 km.

At 5 kph, to cover 9 km. Raja would have taken 1 Hr. 48 Min (a little over 1 hr. 45 min.)

7. Ashish Kumar says:

let speed be x m/s.

by jogging he would have reached in 1 hr 45 mins=105 mis.
he reaches 1 hr 10 mins earlier i.e. 70 mins earlier. hence, he takes 105-70=35 mins.
let time of jogging = a mins. hence, time travelled by taxi = (35-a) mins.

equating distance covered(i.e. to the office) by jogging alone to distance covered by jogging as well as taxi,
105*x=a*x+(35-a)*6x
a=21 mins.

speed of jogging = 9000/(105*60)m/s
hence distance covered by jogging= speed * time= 9000 * 21/(105)= 1800 m= 1.8 km.

8. Mohit says:

Time: 38 min.

Raja’s jogging speed = 5 kph
Car speed = 30 kph

2 km jog: Time = 24 min
7 km car: Time = 14 min

Hence, Raja jogged for 2 km.

9. hitesh mangla says: