100+ Speed, Time and Distance Problems with Solutions - 1

Question: 1

Deepa rides her bike at an average speed of 30 km/hr and reaches her destination in 6 hours. Hema covers the same distance in 4 hours. If Deepa increases her average speed by 10 km/hr and Hema increases her average speed by 5 km/hr, what would be the difference in their time taken to reach the destination?

(A) 40 minutes

(B) 45 minutes

(C) 48 minutes

(D) 54 minutes

Ans: D

Deepa’s original speed = 30 km/hr.

Deepa’s new speed = (30 + 10) km/hr = 40 km/hr.

Distance = (30 × 6)km = 180 km.

Hema’s original speed = $$({180}/{4})$$km/hr = 45 km/hr.

Hema’s new speed = (45 + 5) km/hr = 50 km/hr.

Difference in time = $$({180}/{40} - {180}/{50})$$hrs = $$({9}/{10} × 60)$$min = 54 min.

Question: 2

A train travels at an average of 50 miles per hour for $$2{1}/{2}$$ hours and then travels at a speed of 70 miles per hour for $$1{1}/{2}$$hours. How far did the train travel in the entire 4 hours?

(A) 120 miles

(B) 200 miles

(C) 230 miles

(D) 270 miles

Ans: C

Total distance travelled = [$$(50 × {1}/{2}$$) + $$(70 × {1}/{2})$$]miles.

                                  = (125 + 105)miles = 230 miles.

Question: 3

A long distance runner runs 9 laps of a 400 metres track everyday. His timings (in min) for four consecutive days are 88, 96, 89 and 87 respectively. On an average, how many metres/minute does the runner cover?

(A) 17.78

(B) 27.78

(C) 30

(D) 40

Ans: D

Average speed = $${Total distance covered} / {Total time taken}$$

= $$({4 × 9 × 400} / {88 + 96 + 89 + 87})$$ m/min = $$({14400}/{360})$$m/min. = 40 m/min.

Question: 4

A salesman travels a distance of 50 km in 2 hours and 30 minutes. How much faster, in kilometer per hour, on an average, much he travel to make such a trip in $${5}/{6}$$ hours less time?

(A) 10

(B) 20

(C) 30

(D) 40

Ans: A

Time required = (2 hrs 30 min - 50 min) = 1 hr 40 min = $$1{2}/{3}$$hrs

∴ Required speed = $$(50 × {3}/{5})$$km/hr = 30 km/hr.

Original speed = $$(50 × {2}/{5})$$ = 20 km/hr

Difference in speed = (30 - 20) km/hr = 10 km/hr

Question: 5

A, B and C are on a trip by a car. A drives during the first hour at an average speed of 50 km/hr. B drives during the next 2 hours at an average speed of 48 km/hr. C drives for the next 3 hours at an average speed of 52 km/hr. They reached their destination after exactly 6 hours. Their mean speed was

(A) 50 km/hr

(B) $$50{1}/{3}$$km/hr

(C) $$51{1}/{3}$$km/hr

(D) 52 km/hr

Ans: B

Total distance travelled = (50 × 1 + 48 × 2 + 52 × 3)km = 302 km

Total time taken = 6 hrs.

∴ Mean speed = $$({302}/{6})$$km/hr = $$50{1}/{3}$$km/hr.

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