Question
A boat is traveling downstream along a river at a speed
of 60 km/h. After covering half the total distance, the speed of the river's current increases by 25%. As a result, the boat reaches its destination 15 minutes earlier than it would have under normal conditions. If the total distance to be covered by the boat is 630 km, determine the original speed of the river current.Solution
Let the speed of the stream be 'x' km/h. Original time taken to cover the journey = (630/60) = 10.5 hours So, time taken to cover the first half of the journey = 10.5 ÷ 2 = 5.25 hours Time taken to cover the second half of the journey = 5.25 hours - 15 minutes = 5 hours So, speed of the boat in second half of the journey = (315/5) = 63 km/h So, net change in speed = 63 - 60 = 3 km/h So, 1.25x - x = 3 Or, 0.25x = 3 So, 'x' = 12 Therefore, speed of the steam = 12 km/hÂ
What is the height of an equilateral triangle if each of its sides is 4√3 cm?
- In triangle XYZ, lines XP and PF are medians of triangle XYZ and triangle XZF respectively. If the area of triangle XPF is 15 cm², calculate the area of t...
The area of a triangle is 216 cm² and the ratio of its sides is 9: 12: 15. What is the perimeter of the triangle?
- Find the vertical height from a vertex to the base of an equilateral triangle with a side measuring 12√3 cm.
In a right-angled triangle, the two perpendicular sides are 9 cm and 12 cm. What is the radius of the incircle of the triangle?
Area of a triangles with vertices at (2, 3), (-1, 0) and (2, -4) is :
If area of similar triangles ∆ ABC and ∆ DEF be 64 sq Cm and 121 sq cm and EF = 15.4 cm then BC equals
In a ∆ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠ BAC = 75°, what is the measure of &...
In a triangle ABC, AD is the altitude from A to BC. If AD = 12 cm, AB = 13 cm, and AC = 14 cm, find the length of BC.
Find the length of AB, if ΔABC ~ ΔRQP and BC = 14 cm, QP = 7 cm and RQ = 5 cm.
