Question

Being 10 miles apart, two cars started moving towards each other. After one hour they met, and during that time the first car covered 2 miles more than the second car. What was the speed of the first car?

Answer 1

The speed of the first car was 6 miles/hour

Further explanation

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

Distance between two cars = d = 10 miles

Time Taken = t = 1 hour

Distance covered by the first car = d₁ = 2 + d₂

Unknown:

Speed of the first car = v₁ = ?

Solution:

$d = d_1 + d_2$

$10 = ( 2 + d_2 ) + d_2$

$10 = 2 + 2d_2$

$10 - 2 = 2 d_2$

$8 = 2 d_2$

$d_2 = 8 \div 2$

$d_2 = 4 \texttt{ miles}$

$\texttt{ }$

$d_1 = 2 + d_2 = 2 + 4 = 6 \texttt{ miles}$

$v_1 = d_1 \div t = 6 \div 1 = 6 \texttt{ miles/hour}$

Learn more

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Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

Answer 2

The speed of the first car is $\boxed{6{\text{ mph}}}$ and the speed of the second car is $\boxed{4{\text{ mph}}}.$

Further explanation:

The formula of the speed can be expressed as follows,

$\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}}$

The formula of the time can be expressed as follows,

$\boxed{{\text{Time}} = \frac{{{\text{Distance}}}}{{{\text{Speed}}}}}$

Given:

The distance between the two cars is $10{\text{ miles}}.$

The first car covered 2 miles more than the second car.

Explanation:

Consider the speed of the second car be “$x$”.

Consider the speed of the first car be “$x+2$”.

The distance covered by the first car in one hour is $x + 2{\text{ miles}}.$

The distance covered by the second car in one hour is $x{\text{ miles}}.$

The total distance covered by two cars is $10{\text{ miles}}.$

$\begin{aligned}x + 2 + x &= 10\\2x + 2 &= 10\\2x &= 10 - 2\\2x &= 8\\x&= 4\\\end{aligned}$

The speed of the second car is $4{\text{ miles/h}}.$

The speed of the first car can be obtained as follows,

$\begin{aligned}{\text{Speed}} &= x + 2\\&= 4 + 2\\&= 6{\text{ miles/h}}\\\end{aligned}$

The speed of the first car is $\boxed{6{\text{ mph}}}$ and the speed of the second car is $\boxed{4{\text{ mph}}}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed and Distance

Keywords: 10 miles, speed of first car, speed of the second car, after one hour, moving toward, each other, 2 miles per hour, one hour.