Time, Speed and Distance Questions

Multiple choice
  1. $13$ km/hr
  2. $20$ km/hr
  3. $23$ km/hr
  4. $30$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the speed of the bicycle. The effective speed with the wind is v + 10 and against the wind is v - 10. The time taken is 60/(v+10) + 60/(v-10) = 8. Solving this quadratic equation: 60(v-10 + v+10) = 8(v^2 - 100), which simplifies to 120v = 8v^2 - 800, or v^2 - 15v - 100 = 0. Factoring gives (v-20)(v+5) = 0, so v = 20 km/hr.

Multiple choice
  1. Speed of first train $=$ $20$ km/hr , speed of second train $=$ $15$ km/hr
  2. Speed of first train $=$ $25$ km/hr , speed of second train $=$ $20$ km/hr
  3. Speed of first train $=$ $15$ km/hr , speed of second train $=$ $10$ km/hr
  4. Speed of first train $ = $ $30$ km/hr , speed of second train $=$ $25$ km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed of second train be v. First train is v+5. After 2 hours, distances are 2v and 2(v+5). By Pythagoras, (2v)^2 + (2(v+5))^2 = 50^2. 4v^2 + 4(v^2+10v+25) = 2500. 8v^2 + 40v + 100 = 2500. 8v^2 + 40v - 2400 = 0. v^2 + 5v - 300 = 0. (v+20)(v-15) = 0. v=15. First train = 20, second = 15.

Multiple choice
  1. $2$ hours
  2. $3$ hours
  3. $4$ hours
  4. $5$ hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speeds be J and j. J + j = 9. Time = 20/J + 20/j = 9. 20(J+j)/(J*j) = 9 => 20(9)/(J*j) = 9 => J*j = 20. Roots of x^2 - 9x + 20 = 0 are 4 and 5. Since John is faster, John = 5, Jude = 4. Time for Jude = 20/4 = 5 hours.

Multiple choice
  1. $300\sqrt {5}m$
  2. $300 m$
  3. $300\sqrt {61}m$
  4. $3000m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After 1.5 hours, the north-bound plane travels 1000 * 1.5 = 1500 km, and the west-bound plane travels 1200 * 1.5 = 1800 km. The distance between them is the hypotenuse of a right triangle: sqrt(1500^2 + 1800^2) = sqrt(2250000 + 3240000) = sqrt(5490000) = 300 * sqrt(61) km. The unit in the options is listed as 'm' but should be 'km'.