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The speed of a hare is 6 km/hr faster than that of a tortoise. The hare can travel 40 km in the same time that it takes the tortoise to travel 10 km. Find the speed of the hare.

User Jsaji
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We are given that the velocity of a hare is 6 km/h faster than the velocity of a tortoise. We can represent this as follows:


v_h=6+v_t
\begin{gathered} v_h=\text{ velocity of the hare} \\ v_t=\text{velocity of the tortoise} \end{gathered}

Now, we are also given that the hare travels 40 km using the same time it takes the tortoise to travel 10 km. Since the distance is the product of the velocity by the time, we have:


\begin{gathered} 40km=v_ht \\ 10km=v_tt \end{gathered}

Where:


t=\text{time}

Now, we divide both equations:


(40km)/(10km)=(v_ht)/(v_tt)

Since the time is the same we can cancel out "t":


(40km)/(10km)=(v_h)/(v_t)

Simplifying the fraction:


4=(v_h)/(v_t)

Now, we multiply both sides by the velocity of the tortoise:


4v_t=v_h

Now, we substitute this value in the first equations, we get:


4v_t=6+v_t

Now, we subtract the speed of the tortoise from both sides:


4v_t-v_t=6

Solving the operations:


3v_t=6

Now, we divide both sides by 3:


\begin{gathered} v_t=(6)/(3) \\ \\ v_t=2 \end{gathered}

Therefore, the velocity of the tortoise is 2 km/h.

Now, since the velocity of the hare is 4 times the velocity of the tortoise, we have:


\begin{gathered} v_h=4v_t \\ v_h=4(2(km)/(h)) \\ v_h=8(km)/(h) \end{gathered}

Therefore, the velocity of the hare is 8 km/h.

User JoniJnm
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