A typist can type 146 words in 100 seconds. At this rate, how many minutes and seconds would it take him to type 657 words.

657/146 = x/100

Solve for x and convert to minutes and seconds.

It would take the typist 450 seconds to type 657 words.

To solve this problem, we can set up a proportion using the given information.

Let's represent the number of words typed as "W" and the time taken in seconds as "T".

Based on the information given, we know that the typist can type 146 words in 100 seconds. So we have the ratio:

146 words / 100 seconds

To find out how long it would take the typist to type 657 words, we need to set up the proportion:

146 words / 100 seconds = 657 words / X seconds

Now, we can solve for X (the time taken to type 657 words) by cross-multiplying and then dividing:

146X = 657 * 100

X = (657 * 100) / 146

X ≈ 450 seconds

Now, we have the time taken in seconds, so we need to convert it to minutes and seconds.

To convert seconds to minutes, we divide by 60:

450 seconds / 60 = 7.5 minutes

Since we can't have 0.5 minutes, we will round down to 7 complete minutes.

To find the remaining seconds, we calculate the remainder after dividing by 60:

450 seconds % 60 = 30 seconds

Therefore, it would take the typist approximately 7 minutes and 30 seconds to type 657 words at the given rate.