Question
A bike departs from point X at 9:00 AM toward point Y,
traveling at a speed of 45 km/h. Two hours later, a car starts from point X toward point Y at a speed of 60 km/h. The car overtakes the bike at point Z, located between X and Y. After overtaking the bike, the car reaches point Y in 15 hours and immediately begins its return journey. The car and the bike meet again at point W. Determine the distance between points W and Z.Solution
According to the question, Time taken by car to overtake bike = 2 x 45 / (60 – 45) = 6 hours After 6 hours from start, both are at point Z. Distance between point Z and point Y = 60 x 15 = 900 km In 15, hours distance travelled by bike = 15 x 45 = 675 km Now at this point, the bike is running towards point Y and the car is towards X. Now, time is taken by car to reach at point W after reaching point Y = (900 – 675)/ (60 + 45) = 15/7 hours Distance between point W and Z = 900 – 15/7 x 60 = 771.42 km Hence answer is option A
The vertices of a triangle are given as (5, 4), (9, 6), and (1, 5). Determine the area enclosed by this triangle.
In a right-angled triangle, the perimeter is 60 cm. If the base is 12 cm and the height is 16 cm, find the length of the hypotenuse.
In a triangle ABC, the incenter is at O. Find angle BAC if angle BOC=120°.
- The base of a right pyramid is an equilateral triangle with side 7 cm. If the height of the pyramid is 32√3 cm, then find the volume of the pyramid.
- The base of a right pyramid is an equilateral triangle with side 12 cm. If the height of the pyramid is 40√3 cm, calculate the volume of the pyramid.
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 &...
The area (in square units) of the triangle formed by the vertices (0,2), (2,3), and (3,1) is:
In ∆ PQR, S is the midpoint of QR. T is the midpoint of line PS. Then, Area of ∆PTQ : Area of ∆ PQR is
In triangle ABC, the lengths of its sides are given as AB = 8 cm, AC = 10 cm, and BC = 12 cm. Determine the length of the median drawn from vertex 'A' t...
The area of an equilateral triangle is 64√3 cm2. Find the radius of the circle that circumscribes the triangle.
