Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Let the speed of the train be x km/hour that of the bus be y km/hr, we have the following cases
Case I: When Roohi travels 300 Km by train and the rest by bus
Time taken by Roohi to travel $60 \mathrm{Km}$ by train $=\frac{60}{x} h r s$
Time taken by Roohi to travel $(300-60)=240 \mathrm{Km}$ by bus $=\frac{240}{y} h r s$
Total time taken by Roohi to cover $300 \mathrm{Km}=\frac{60}{x}+\frac{240}{y}$
It is given that total time taken in 4 hours
$\frac{60}{x}+\frac{240}{y}=4$
$60\left(\frac{1}{x}+\frac{4}{y}\right)=4$
$\left(\frac{1}{x}+\frac{4}{y}\right)=\frac{4}{60}$
$\frac{1}{x}+\frac{4}{y}=\frac{1}{15} \cdots(i)$
Case II: When Roohi travels 100 km by train and the rest by bus
Time taken by Roohi to travel $100 \mathrm{Km}$ by train $=\frac{100}{x} h r s$
Time taken by Roohi to travel $(300-100)=200 \mathrm{Km}$ by bus $=\frac{200}{y} h r s$
In this case total time of the journey is 4 hours 10 minutes
$\frac{100}{x}+\frac{200}{y}=4 h r s 10 \mathrm{~min}$ utes
$\frac{100}{x}+\frac{200}{y}=4 \frac{10}{60}$
$\frac{100}{x}+\frac{200}{y}=\frac{25}{6}$
$100\left(\frac{1}{x}+\frac{2}{y}\right)=\frac{25}{6}$
$\frac{1}{x}+\frac{2}{y}=\frac{25}{6} \times \frac{1}{100}$
$\frac{1}{x}+\frac{2}{y}=\frac{1}{24}$$\ldots$ (i)
Putting $\frac{1}{x}=u$ and $\frac{1}{y}=u$, the equations $(i)$ and $(i i)$ reduces to
$1 u+4 v=\frac{1}{15} \cdots(i i i)$
$1 u+2 v=\frac{1}{24} \cdots(i v)$
Subtracting equation (iv) from (iii)we get
$2 v=\frac{24-15}{360}$
$2 v=\frac{9}{360}$
$2 v=\frac{9}{360}$
$v=\frac{1}{40} \times \frac{1}{2}$
$v=\frac{1}{80}$
Putting $v=\frac{1}{80}$ in equation (iii), we get
$1 u+4 v=\frac{1}{15}$
$1 u+4 \times \frac{1}{80}=\frac{1}{15}$
$1 u+\frac{4}{80}=\frac{1}{15}$
$1 u=\frac{1}{15}-\frac{4}{80}$
$1 u=\frac{1}{15}-\frac{1}{20}$
$1 u=\frac{20-15}{300}$
$1 u=\frac{5}{300}$
$u=\frac{1}{60}$
Now
$u=\frac{1}{60}$
$\frac{1}{x}=\frac{1}{60}$
$x=60$
and
$v=\frac{1}{80}$
$\frac{1}{y}=\frac{1}{80}$
$y=80$
Hence, the speed of the train is $60 \mathrm{~km} / \mathrm{hr}$,
The speed of the bus is $80 \mathrm{~km} / \mathrm{hr}$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,