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# [Smart Math] Time Speed Distance Problem 15

Here’s and example of a SMART MATH problem for TIME SPEED DISTANCE.

### Problem

Mira rowed upstream in a stream flowing at the rate of 1.5 km/hr to a certain point and then rowed back stopping 2 kms short of the place where she originally started. If the rowing time was 2 hours 20 minutes and her uniform speed in still water was 4.5 km/hr, how far upstream did she go?

1. 4.25 kms
2. 5.33 kms
3. 6.50 kms
4. 7.00 kms
5. 8.75 kms

### The Usual Method

Speed of Mira in still water = 4.5 km/hr.

Speed of stream = 1.5 km/hr

Hence upstream travel speed = 4.5 – 1.5 = 3 km/hr

And downstream travel speed = 4.5 + 1.5 = 6 km/hr

Let the distance traveled upstream = x kms.

Time taken to travel upstream = $\frac{x}{3}$hours

Time taken to travel downstream = $\frac{x-2}{6}$hours

Total time taken = $\frac{x}{3}$ + $\frac{x-2}{6}$ = 2 hours 20 minutes

$\therefore \frac{x}{3}+\frac{(x-2)}{6}=2\frac{1}{3}$

$\therefore \frac{3x-2}{6}=\frac{7}{3}$

$\therefore 3x-2=14$

$\therefore x=\frac{16}{3}=$ 5.33 kms

(Ans: 2)

Estimated Time to arrive at the answer = 75 seconds.

### Using Technique

Since the upstream travel speed = 4.5 – 1.5 = 3 km/hr and downstream travel speed = 4.5 + 1.5 = 6 km/hr (both being integers), but total travel time = $2\frac{1}{3}$hours (being a fraction with denominator as 3), the answer should also be a fraction with denominator as 3. The only answer satisfying this condition is 5.33 kms.