Q) The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more for upstream than downstream.
1. Let speed of the stream be x km/hr. Then speed of the motorboat in upstream will be
a) 20 km/hrĀ Ā Ā Ā Ā Ā b) (20 + x) km/hrĀ Ā Ā Ā Ā c) (20 – x) km/hrĀ Ā Ā Ā Ā Ā d) 2 km/hr
2. What is the relation between speed, distance and time?
a) speed = (distance )/timeĀ Ā Ā Ā Ā b) distance = (speed )/time
c) time = speed x distanceĀ Ā Ā Ā Ā d) speed = distance x time
3. Which is the correct quadratic equation for the speed of the current?
a) x2 + 30x ā 200 = 0Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā b) x2 + 20x ā 400 = 0
c) x2 + 30x ā 400 = 0Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā d) x2 ā 20x ā 400 = 0
4. What is the speed of current?
a) 20 km/hourĀ Ā Ā Ā b) 10 km/hourĀ Ā Ā Ā Ā Ā c) 15 km/hourĀ Ā Ā Ā Ā Ā Ā d) 25 km/hour
5. How much time boat took in downstream?
a) 90 minuteĀ Ā Ā Ā Ā b) 15 minuteĀ Ā Ā Ā Ā Ā Ā Ā c) 30 minuteĀ Ā Ā Ā Ā Ā Ā Ā Ā d) 45 minute
Ans:
1.Ā
āµ Upstream speed = Boat’s speed – Stream’s speed
ā“ Upstream speed = 20 km/hr – x km/hr
= (20 – x) km/hr
Therefore, option (c) is correct.
2.Ā
Speed is always given by
Therefore, option (a) is correct.
3.
Step 1: By given information, Boat’s speed = 20 km/hr and Stream’s speed = X km/hr
ā“ Upstream speed = (20 – X) km/hr
and Downstream speed = (20 + X) km/hr
Step 2: Since distance travelled is D
Since, time taken to travel =
ā“ Time taken upstream =
Similarly,Ā Time taken downstream =
Step 3: By given condition: Upstream time is 1 hour more than downstream time
ā“
ā“
ā“
ā“ 15 (20 + X) = (35 + X)(20 – X)
ā“ 300 + 15 X =Ā 700 + 20 X – 35 X – X2
ā“ X2 + 30 X – 400 = 0
Therefore, option (c) is correct.
4. Let’s solve above quadratic equation:
By mid term splitting we get:
ā“ X2 + 40 X – 10 X – 400 = 0
ā“ X (X + 40) – 10 (X + 40) = 0
ā“ (X + 40) (X – 10) = 0
ā“ X = 10 and X = – 40
Here, we reject X = – 40 because the speed value has to be positive and accept X = 10
Hence, speed of the current is 10 km/hr
Therefore, Option (b) is correct
5.Ā As calculated in part 3, Time taken downstream =
Since X = 10, ā“ the Time taken downstream
=
=
= 0.5 hrs = 30 mins
Therefore, option (c) is correct.
Check: Time taken upstream = 
= 1.5 hrs We just calculated: Time taken downstream = 0.5 hrs
Here, upstream time = downstream time + 1
Since it matches with the given condition in question, hence our answer is correct.Ā
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= 0.5 hrs = 30 mins
= 1.5 hrs