Question

A jet flew from Tokyo to Bangkok, a distance of 200 km. On the return trip, the speed was decreased by 50 kmph. If the difference in the time of the flights was 2 hours. How much time will it take from Tokyo to Bangkok?

A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hour

Answer 1

Hint- Distance is the measurement of the length of the path travelled by the body to reach the destination. In this question, we need to determine the time taken by the flight to travel a distance of 200 km in the onward journey, i.e., from Tokyo to Bangkok for which we have to determine the velocity of the flight first by using the general formula ${\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}$. Here, two conditions are given, which must satisfy the equations generated in solving the problem.


Complete step by step solution:
Distance between Tokyo and Bangkok is 200 km.
When the jet flew from Tokyo to Bangkok, let the time taken be ‘${t_1}$’ hours and speed be ‘$x$’ kmph.
Substitute 200 for the distance in the formula ${\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}$ to establish a relation between the time and the velocity as:

$
  {\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}} \\
  {t_1} = \dfrac{{200}}{x} - - - - (i) \\
 $

When the jet flew from Bangkok to Tokyo, let the time taken be ‘${t_2}$’ hours and speed be ‘\[x - 50\]’ kmph.
Again, substitute 200 for the distance in the formula ${\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}$ to establish a relation between the new time and the new velocity as:
${t_2} = \dfrac{{200}}{{x - 50}} - - - - (ii)$

According to the question, it is already mentioned the difference between ${t_1}$ and ${t_2}$ is 2 hours so,
$
  {t_1} - {t_2} = 2 \\
  \dfrac{{200}}{x} - \dfrac{{200}}{{x - 50}} = 2 \\
  200\left( {\dfrac{1}{x} - \dfrac{1}{{x - 50}}} \right) = 2 \\
  100\left( {\dfrac{{x - 50 - x}}{{x(x - 50)}}} \right) = 1 \\
  {x^2} - 50x + 5000 = 0 \\
  {x^2} - 100x + 50x + 5000 = 0 \\
  x(x - 100) + 50(x + 100) = 0 \\
  (x - 100)(x + 50) = 0 \\
  x = 100; - 50 \\
 $

As the speed cannot be negative, that’s why we neglect -50, and thus, the speed of the flight is$x = 100{\text{ }}kmph$.

Substitute $x = 100{\text{ }}kmph$ in equation (i) to compute the time taken by the flight to reach Tokyo from Bangkok as:

$
  {t_1} = \dfrac{{200}}{x} \\
   = \dfrac{{200}}{{100}} \\
   = 2{\text{ }}hrs \\
 $

Hence, the time taken by the flight on the onward journey from Tokyo to Bangkok is 20 hours.
Option B is correct.


Note: Distance and displacement are two different parameters. Here, as the flight is returning back to Tokyo, so, the net displacement is zero whereas the net distance travelled by the flight is 400 km.