Speed Time And Distance - Study Mode
[#1] A car runs first 275 km at an average speed of 50 km/h and the next 315 km at an average speed of 70 km/h. What is the average speed (in km/h) for the entire journey?
Correct Answer
(C) 59
Explanation
Solution: Time taken to cover 275 km = $$frac{{275}}{{50}}$$xa0h = 5.5 h Time taken to cover 315 km = $$frac{{315}}{{70}}$$xa0h = 4.5 h Average speed of entire journey $$eqalign{
& = frac{{{ ext{Total distance}}}}{{{ ext{Total time taken}}}} cr
& = frac{{590}}{{10}} cr
& = 59{ ext{ Answer}} cr} $$
[#2] R jogs at twice the speed of walking and runs at twice the speed of jogging. From his home to office, he covers half of the distance by walking and the rest by jogging. From his office to home, he covers half the distance jogging and the rest by running. What is his average speed (in km/h) in a complete round from his home to office and back home if the distance between his office and home is 10 km and he walks at the speed of 5 km/h?
Correct Answer
(D) $$frac{{80}}{9}$$
Explanation
Solution: Walking speed = 5 kmph Jogging speed = 10 kmph Running speed = 20 kmph $$eqalign{
& { ext{Average speed}} = frac{{20}}{{frac{5}{5} + frac{5}{{10}} + frac{5}{{10}} + frac{5}{{20}}}} cr
& = frac{{20}}{{2 + frac{5}{{20}}}} cr
& = frac{{20 imes 20}}{{45}} cr
& = frac{{80}}{9}{ ext{ kmph}} cr} $$
[#3] The driver of a car, which is travelling at a speed of 75 km/hr locates a bus 80 m ahead of him, travelling in the same direction. After 15 seconds, he finds the bus is 40 m behind the car. What is the speed of the bus (in km/hr)?
Correct Answer
(B) 46.2
Explanation
Solution: Let speed of the bus = x Relative speed in same direction = 75 - x Total distance = 80 + 40 = 120 m $$eqalign{
& { ext{Speed}} = frac{{{ ext{Distance}}}}{{{ ext{Time}}}} cr
& 75 - x = frac{{120}}{{15}} imes frac{{18}}{5} cr
& 75 - x = frac{{144}}{5} cr
& 75 - x = 28.8 cr
& x = 75 - 28.8 cr
& x = 46.2{ ext{ km/hr}} cr} $$
[#4] A train without stoppage travels with an average speed of 80 km/h and with stoppage, it travels with an average speed of 64 km/h. For how many minutes does the train stop on an average per hour?
Correct Answer
(A) 12
Explanation
Solution: $$eqalign{
& left( {frac{{{ ext{Faster speed}} - { ext{Slower speed}}}}{{{ ext{Faster speed}}}} imes 60}
ight){ ext{min/hr}} cr
& = frac{{80 - 64}}{{80}} imes 60 cr
& = frac{{16}}{{80}} imes 60 cr
& = 12{ ext{ min}} cr} $$
[#5] A is chasing B in the same interval of time. A jumps 8 times, while B jumps 6 times. But the distance covered by A in 7 jumps is the same as that of B in 5 jumps. The ratio between the speeds of A and B is . . . . . . . .
Correct Answer
(C) 20 : 21
Explanation
Solution: [x08egin{array}{*{20}{c}}
{}&{ ext{A}}&:&{ ext{B}} \
{{ ext{Time}}}&8&{}&6
end{array}] And 7 × A = B × 5 Distance A : B = 5 : 7 [x08egin{array}{*{20}{c}}
{{ ext{Ratio}}}&{ ext{A}}&:&{ ext{B}} \
{}&8&:&6 \
{}&5&:&7 \
{}&{overline {,40,} }&{}&{overline {,42,} } \
{}&{20}&:&{21}
end{array}]