algebra

The product of \(\frac{1}{4}\) and \(\frac{1}{5}\) of a number is \(500\). What is the number?

If \(3\) is subtracted from the numerator of a certain fraction, the value of the fraction becomes \(3/5\). If \(1\) is subtracted from the denominator of the same fraction, it becomes \(2/3\). Find the original fraction.

The denominator of a certain fraction is three more than twice the numerator. If \(7\) is added to both terms of the fraction, the resulting fraction is \(3/5\). Find the original fraction.

Find the product of two numbers such that twice the first added to the second equals \(19\) and three times the first is \(21\) more than the second.

The tens' digit of a number is \(3\) less than the units' digit. If the number is divided by the sum of the digits, the quotient is \(4\) and the remainder is \(3\). What is the original number?

The second of the four numbers is three less than the first, the third is four more than the first and the fourth is two more than the third. Find the fourth number if their sum is \(35\).

A jogger starts a course at a steady rate of \(8\) kph. Five minutes later, a second jogger starts the same course at \(10\) kph. How long will it take the second jogger to catch the first?

A boat man rows to a place \(4.8\) miles with the stream and back in \(14\) hours, but finds that he can row \(14\) miles with the stream in the same time as \(3\) miles against the stream. Find the rate of the stream.

A man rows downstream at the rate of \(5\) mph and upstream at the rate of \(2\) mph. How far downstream should he go if he is to return in \(7/4\) hours after leaving?

An airplane flying with the wind, took \(2\) hours to travel \(1000\) km and \(2.5\) hours in flying back. What was the wind velocity in kph?

A boat travels downstream in \(2/3\) of the time as it goes going upstream. If the velocity of the river's current is \(8\) kph, determine the velocity of the boat in still water.

Two planes leave Manila for a southern city, a distance of \(900\) km. Plane A travels at a ground speed of \(90\) kph faster than the plane B. Plane A arrives in their destination \(2\) hours and \(15\) minutes ahead of Plane B. What is the ground speed of plane A?

A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at \(3/5\) of its former rate and arrives three hour after time; but had the accident happened \(50\) miles farther on the line, it would have arrived one and one-half hour sooner. Find the length of the journey.

On a certain trip, Edgar drive \(231\) km in exactly the same time as Erwin drive \(308\) km. If Erwin's rate exceeded that of Edgar by \(13\) kph, determine the rate of Erwin.

In how many minutes after 2 o'clock will the hands of the clock extend in opposite directions for the first time?

In how many minutes after 7 o'clock will the hands be directly opposite each other for the first time?

What time after 3 o'clock will the hands of the clock be together for the first time?

At what time after 12:00 noon will the hour hand and minute hand of the clock first form an angle of \(120^\circ\)?

At what time between 8 and 9 o'clock will the minute hand coincide with the hour hand?

A man left his home at past 3:00 o'clock PM as indicated in his wall clock, between 2 to 3 hours after, he returns home and noticed the hands of the clock interchanged. At what time did the man leave his home?