This is a continuation of article on tricks to solve questions related to time and distance in quantitative aptitude examinations. In this part of tutorial we’ll learn about some of the important concepts for solving problems related to boats and streams, escalators and journey with stoppage.
Objectives
- Boats and streams
- Escalators
- Journey with stoppages
- Speed of moving bodies as per the speed of sound
- Understanding and visualizing the situation.
- Effective practical application of the concept of relative speed.
Important Terminologies
Speed of boat in still water (b): Speed of the boat in the still water is the real speed of the boat without any additional supportive or resistive forces.
Speed of current/ stream / wave (c): This is the speed of water flow.
Downstream speed (v): If the boat is moving along with the direction of the flow then the effective speed of the boat is called downstream speed.
Downstream speed = sped of the boat in still water + speed of the stream; `v = b + c`
Upstream speed (u): If the boat is moving against the direction of the stream, then the effective speed of boat is called the upstream speed.
Upstream speed = speed of boat in still water - speed of the stream; `u = b - c`
`-> "Speed of boat in still water" = ("upstream speed" + "downstream speed")/2`
`(u - v)/2 = ((b - c) - (b + c))/2 = c`
`-> "Speed of stream" = ("downstream speed" - "upstream speed")/2`
A very useful illustration of the relationship between basic parameters
As per the above explanations, it is easy to observe that the Upstream Speed (u), Speed of the boat in still water (b) and the Downstream speed (v) are the three consecutive terms in an Arithmetic Progression in the mentioned increasing order, with a common difference which is the Speed of the Stream (c). image
`"Speed of Boat in Still Water " + " Speed of Stream " = " Downstream Speed"`
Escalators
This is most repeating type of questions in quant area of CAT, MAT and CMAT exams. Concept of escalators is same as the concept of downstream and upstream.
Let the speed of a person when he is walking with the escalator (both moving up or down) ` = s` and speed of the moving escalator `= e`
Case I: An escalator is moving up at a speed of 'e'
`= "Normal speed of the person" + "speed of escalator"`
`= s + e`
`= s - e`
Case II: An escalator is moving down at a speed of 'e'.
`= s - e`
`= s + e`
Concept review questions
Let the speed of stream `= c kmph`
Upstream speed `= (20 - c) kmph`
Downstream speed `= (20 + c) kmph`
`"Upstream speed"/"Downstream speed" = (20 -c)/(20 + c) = 4/5`
On solving this, we'll get `c = 20/9 = 2.22 kmph`
Alternate Method:
`-> 20/c = (5 + 4)/ (5 - 4)`
`-> c = 20/9 = 2.22 kmph`
Speed of current `= 5 kmph`
Speed of boat in still water `= 30 + 5 = 35 kmph`
Downstream speed `= 35 + 5 = 40 kmph`
Let the speed of Abijith `= s "m/s"`
And the speed of escalator `= e "m/s"`
Time taken by Abijith for moving upward `= 10 sec`
`s + e = 32/10 = 3.2 "m/s" -> (1)`
Note that the speed of Abijith is more than that of escalator, and then only he can move against the escalator and reach down.
Time taken by Abijith for moving downward `= 16 sec``s - e = 32/16 = 2 "m/s" -> (2)`
From equation (1) and (2), `s = 2.6 "m/s"`
Hence speed of Abhjit is `2.6 "m/s"`
Upstream speed `= s - 2 kmph = 8 kmph`
`-> s = 10 kmph`
Downstream speed `= s + 2 = 12 kmph`
Average speed `= (2 xx 8 xx 12)/(8 + 12) = 9.6kmph`
