Question

A car is covering a distance of $ 170km\,\,in\,2\, $ hours, partly at a speed of $ 100km/hr $ and partly at $ 50km/hr $ . The distance that is travelled at the speed of A $ 50\,km/hr $ will be:
A. $ 50\,km $ $ 50\, $ $ $
B. $ 40\,km $
C. $ 30\,km $
D. $ 60\,km $

Answer 1

Hint:Since the distance is covered partly in different speeds, we need to suppose the distance covered at these different cities and then deduct the equation out using the formula. Also, we will be solving this question in two ways in order to verify our solution and getting a clear view for this question.

Complete step-by-step answer:
(A)
Given that,
Total distance D $ = 170km $
Time t $ = 2\,hr $
Partly speed $ = 100km/hr $
Partly speed $ = 50\,km/hr $
Let us consider $ x $ distance covered by speed of $ 50km/hr $ and $ 170 - x $ distance covered by speed $ 100km/hr $
So, the time for $ x $ distance
  $ {t_x} = \dfrac{{x\,km}}{{50\,km/hr}} $
The time for $ 170 - x $ distance
  $ {t_{170}} = \dfrac{{\left( {170 - x} \right)km}}{{100\,km/hr}} $
Now, the total time
  $ t = {t_x} + {t_{170 - x}} $
  $
  2 = \dfrac{x}{{50}} + \dfrac{{170 - x}}{{100}} \\
  2x + 170 - x = 2 \\
  x = 30\,km \\
  $

Now let’s verify our solution by solving it in a different way.
(B)
Let the distance travelled at $ 100\,km/hr $ be $ x\,km $ .
Then, distance travelled at $ 50\,km/hr $ is $ \left( {170 - x} \right)km $.
Given, $ \dfrac{x}{{100}} + \dfrac{{\left( {170 - x} \right)}}{{50}} = 2 $
  $ \Rightarrow \dfrac{{x + 2\left( {170 - x} \right)}}{{100}} = 2 $ G
  $ \Rightarrow x + 340 - 2x = 200 $
  $ \Rightarrow x = 140km $
Distance travelled at 100km/hr=140km
Distance travelled at 50km/hr
  $
  \, = \left( {170 - 140} \right)km \\
   = 30km \\
  $
Hence, the answer of the solution is option C. 30km

Note:Speed here is directly proportional to distance, therefore we will take distance according to the speed proportionally and then solve it using equations in accordance with total time i.e. 2 hours. The distance that is covered per unit time is called speed. Speed is directly proportional to distance and inversely to time as it is clear in the formula.
Speed =Distance/time
Time =Distance/Speed
Distance=speed $ \times $ time
Conversion of units -
 $ 1km/hr = 5/18\,m/\sec $
 $ 1\,m/\sec = 18/5\,km/hr $
 $ 1\,km/hr = 5/8\,mile/hr $
 $ 1\,mile/hr = 22/15\,foot/second $