Speed Time And Distance - Study Mode

[#291] To reach point B from point A at 4 pm, Sara will have to travel at an average speed of 18 kmph. She will reach point B at 3 pm if she travels at an average speed of 24 kmph. At what average speed should Sara travels to reach point B at 2 pm ?
Correct Answer

(A) 36 km/hr

Explanation

Solution: Difference between time = 1 hour Distance between point AB = x km According to the question, $$ Rightarrow frac{x}{{18}} - frac{x}{{24}} = 1$$ L.C.M. of 18 and 24 = 72 $$eqalign{
& Rightarrow frac{{4x - 3x}}{{72}} = 1 cr
& Rightarrow x = 72{ ext{ km}} cr} $$ Time taken at 18 km/hr to cover 72 km $$ = frac{{72}}{{18}} = 4{ ext{ hours}}$$ ∴ Speed to cover 72 km in 2 hours : $$ = frac{{72}}{2} = 36{ ext{ km/hr}}$$

[#292] A person travels three equal distance at a speed of x km/hr, y km/hr and z km/hr respectively. What is the average speed for the whole journey ?
Correct Answer

(D) $$frac{{3xyz}}{{left( {xy + yz + zx} ight)}}$$ xa0 xa0km/hr

Explanation

Solution: Let each distance be equal to d Then, total distance travelled = 3d Total time taken : $$eqalign{
& = left( {frac{d}{x} + frac{d}{y} + frac{d}{z}}
ight){ ext{hr}} cr
& = frac{{dleft( {xy + yz + zx}
ight)}}{{xyz}}{ ext{ hr}} cr} $$ ∴ Average speed : $$eqalign{
& = left[ {3d imes frac{{xyz}}{{dleft( {xy + yz + zx}
ight)}}}
ight]{ ext{km/hr}} cr
& = frac{{3xyz}}{{left( {xy + yz + zx}
ight)}}{ ext{ km/hr}} cr} $$

[#293] A car takes 15 minutes less to cover a distance of 75 km, if it increases its speed by 10 km/hr from its usual speed. How much time would it take to cover a distance of 300 km using this speed ?
Correct Answer

(A) 5 hrs

Explanation

Solution: Let the usual speed be x km/hr Then, $$eqalign{
& Leftrightarrow frac{{75}}{x} - frac{{75}}{{x + 10}} = frac{{15}}{{60}} cr
& Leftrightarrow xleft( {x + 10}
ight) = 3000 cr
& Leftrightarrow {x^2} + 10x - 3000 = 0 cr
& Leftrightarrow left( {x + 60}
ight)left( {x - 50}
ight) = 0 cr
& Leftrightarrow x = 50 cr} $$ ∴ Required time : $$eqalign{
& = left( {frac{{300}}{{60}}}
ight){ ext{hrs}} cr
& = 5{ ext{ hrs}} cr} $$

[#294] A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 metres ahead of the policeman, then the time required for the policeman to catch the thief will be :
Correct Answer

(B) 3 minutes

Explanation

Solution: Relative speed = (10 - 8) km/hr = 2 km/hr Required time = Time taken to cover 100 m at relative speed : $$eqalign{
& = left( {frac{{100}}{{2000}}}
ight){ ext{hr}} cr
& = left( {frac{1}{{20}}}
ight){ ext{hr}} cr
& = left( {frac{1}{{20}} imes 60}
ight){ ext{min}} cr
& = 3 ext{ minutes} cr} $$

[#295] Two planes move along a circle of circumference 1.2 kms with constant speeds. When they move in different directions, they meet every 15 seconds and when they move in the same direction one plane overtakes the other every 60 seconds. The speed of the slower plane is :
Correct Answer

(B) 0.03 km/sec

Explanation

Solution: Let their speeds be x m/sec and y m/sec respectively. Then, $$eqalign{
& frac{{1200}}{{x + y}} = 15 cr
& Rightarrow x + y = 80.....(i) cr} $$ And, $$eqalign{
& frac{{1200}}{{x - y}} = 60 cr
& Rightarrow x - y = 20.....(ii) cr} $$ Adding (i) and (ii), we get : 2x = 100 or x = 50 Putting x = 50 in (i), we get : y = 30 Hence, speed of slower plane : = 30 m/sec = 0.03 km/sec